Illustration of an angle

Angle

Illustration of an angle

A diagram illustrating the airplane's angle of incidence at axis A, direction of motion and thrust.

Plane Angle of Incidence

A diagram illustrating the airplane's angle of incidence at axis A, direction of motion and thrust.

The diagram illustrating the plane's angle of incidence pointing down at the motion axis. The plan will exert momentum and thrust force from angle of incidence.

Plane Pointing Down Angle of Incidence

The diagram illustrating the plane's angle of incidence pointing down at the motion axis. The plan will…

"The angle under which the rays of light, coming from the extremities of an object, cross each other at the eye, bears a proportion directly to the length, and inversely to the distance of the object." -Comstock 1850

Angle of Vision

"The angle under which the rays of light, coming from the extremities of an object, cross each other…

An illustration showing an angle the is less than a right angle. This is an acute angle.

Acute Angle

An illustration showing an angle the is less than a right angle. This is an acute angle.

Illustration to show that if an angle is bisected, and if a line drawn through the vertex perpendicular to the bisector, this line forms equal angles with the sides of the given angle.

Bisected Angle

Illustration to show that if an angle is bisected, and if a line drawn through the vertex perpendicular…

Illustration to show that the bisectors of two supplementary adjacent angles are perpendicular to each other.

Bisected Angles

Illustration to show that the bisectors of two supplementary adjacent angles are perpendicular to each…

Illustration to show that the bisector of one of two vertical angles bisects the other.

Bisected Angle

Illustration to show that the bisector of one of two vertical angles bisects the other.

Illustration to show that the bisector of two pairs of vertical angles formed by two intersecting lines are perpendicular to each other.

Bisected Angles

Illustration to show that the bisector of two pairs of vertical angles formed by two intersecting lines…

Illustration to show that the bisector of the vertical angle of an isosceles triangle bisects the base, and is perpendicular to the base.

Bisected Vertical Angle of an Isosceles Triangle

Illustration to show that the bisector of the vertical angle of an isosceles triangle bisects the base,…

Illustration to show that if through any point in the bisector of an angle a line is drawn parallel to either of the sides of the angle, the triangle thus formed is isosceles.

Angle Bisector Drawn Parallel to A Side

Illustration to show that if through any point in the bisector of an angle a line is drawn parallel…

Illustration of construction to lay off an angle.

Construction of Angle

Illustration of construction to lay off an angle.

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector are equal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point in its bisector…

Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its bisector are unequal."

Perpendiculars To The Sides Of An Angle

Illustration used to show "The two perpendiculars to the sides of an angle from any point not in its…

An illustration showing a straight angle. When the sides of an angle extend in opposite directions, so as to be in the same straight line, the angle is called a straight angle.

Straight Angle

An illustration showing a straight angle. When the sides of an angle extend in opposite directions,…

Trihedral angle. "The sum of any two face angles of a trihedral angle is greater than the third face angle."

Trihedral Angle

Trihedral angle. "The sum of any two face angles of a trihedral angle is greater than the third face…

Illustration showing two positive angles; angle 1 being the acute angle and angle 2 being the reflex angle.

Acute and Reflex Angles

Illustration showing two positive angles; angle 1 being the acute angle and angle 2 being the reflex…

An illustration showing acute, obtuse, straight, right, and reflex angles.

Acute, Obtuse, Straight, Right, And Reflex Angles

An illustration showing acute, obtuse, straight, right, and reflex angles.

An illustration of two angles that are adjacent. They have the same vertex and a common side between them. Angles BOD and AOD are adjacent

Adjacent Angles

An illustration of two angles that are adjacent. They have the same vertex and a common side between…

Angles 1 and 2 are adjacent angles. Two angles with a common vertex and a common side between them are adjacent angles.

Adjacent Angles

Angles 1 and 2 are adjacent angles. Two angles with a common vertex and a common side between them are…

Complementary angles

Complementary Angles

Complementary angles

Illustration of complementary angles. Two angles whose sum is a right angle.

Complementary Angles

Illustration of complementary angles. Two angles whose sum is a right angle.

Illustration used to prove that all right angles are equal.

Equal Right Angles

Illustration used to prove that all right angles are equal.

The evolute spiral angle is a wave pattern that mimics the wave of the sea.

Evolute Spiral Angles

The evolute spiral angle is a wave pattern that mimics the wave of the sea.

The evolute spiral angle is a wave pattern that mimics the wave of the sea.

Evolute Spiral Angles

The evolute spiral angle is a wave pattern that mimics the wave of the sea.

An illustration showing an angle the is greater than a right angle and less than a straight angle. This is an obtuse angle (solid curved arrow). The angle that is greater than a straight angle and less than two straight angles is called a reflex angle (dashed curved arrow).

Obtuse And Reflex Angles

An illustration showing an angle the is greater than a right angle and less than a straight angle. This…

Illustration of angles with parallel corresponding sides.

Angles With Parallel Sides

Illustration of angles with parallel corresponding sides.

Illustration of angles with parallel sides going in the opposite direction.

Angles With Parallel Sides

Illustration of angles with parallel sides going in the opposite direction.

Illustration of angles with parallel sides. "GH is parallel to and lies in the same direction as DE, and HI is parallel to but lies in the opposite direction to EF; hence, angle GHI is the supplement of DEF."

Angles With Parallel Sides

Illustration of angles with parallel sides. "GH is parallel to and lies in the same direction as DE,…

Illustration showing four angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 4 Angles

Illustration showing four angles that can be used to define different relationships, such as adjacent,…

Illustration showing four angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 4 Angles

Illustration showing four angles that can be used to define different relationships, such as adjacent,…

Illustration showing six angles that can be used to define different relationships, such as adjacent, supplementary, etc..

Relationships Between 6 Angles

Illustration showing six angles that can be used to define different relationships, such as adjacent,…

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of the sines and cosines of the angles.

Sum of 2 Acute Angles

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of…

Illustration of the superposition of two angles to compare magnitudes of the same kind.

Superposition of Angles

Illustration of the superposition of two angles to compare magnitudes of the same kind.

Supplementary angles

Supplementary Angles

Supplementary angles

Illustration of supplementary angles. Two angles whose sum is a straight angle.

Supplementary Angles

Illustration of supplementary angles. Two angles whose sum is a straight angle.

Illustration of supplementary angles. Two angles whose sum is a straight angle. This can be used tow show the Theorem: If two adjacent angles have their exterior sides in a straight line, these angles are supplementary.

Supplementary Angles

Illustration of supplementary angles. Two angles whose sum is a straight angle. This can be used tow…

Illustration of supplementary angles. Two angles whose sum is a straight angle. This can be used tow show the Theorem: If two adjacent angles are supplementary, their exterior sides are in the same straight line.

Supplementary Angles

Illustration of supplementary angles. Two angles whose sum is a straight angle. This can be used tow…

Illustration that can be used to show supplementary angles. The angles form a straight line.

Supplementary Angles

Illustration that can be used to show supplementary angles. The angles form a straight line.

Illustration of supplementary angles. Angles LMK and KMH are supplementary.

Supplementary Angles

Illustration of supplementary angles. Angles LMK and KMH are supplementary.

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also, Angles ACD and DCB are right angles.

Supplementary and Right Angles

Illustration showing angles 1 and 2 are supplementary and angles ACD and DCB are supplementary. Also,…

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations of the sides of the other. In this illustration, a and b are vertical angles and c and d are vertical angles.

Vertical Angles

Vertical angles are when two angles have the same vertex, and the sides of the one are prolongations…

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or supplementary.

Angles With Parallel Sides

Illustration of two angles whose sides are parallel, each to each, to show they are either equal or…

Illustration showing arcs measured in positive and negative angles.

Positive and Negative Arcs in Circles

Illustration showing arcs measured in positive and negative angles.

Bevel, is a and tool consisting of two rules that are hinged together so you can draw or measure angles of any size. A sliding T bevel is an adjustable gauge for setting and transferring angles. The handle is usually made of wood or plastic and is connected to a metal blade with a thumbscrew or wing nut.

Bevel Square

Bevel, is a and tool consisting of two rules that are hinged together so you can draw or measure angles…

Illustration showing that the bisector of a given angle is the locus of points equidistant from the sides of the angle.

Angle Bisector

Illustration showing that the bisector of a given angle is the locus of points equidistant from the…

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant from the extremities of the line.

Perpendicular Bisector of a Line

Illustration showing that the perpendicular bisector of a given line is the locus of points equidistant…

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is less than the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is equal to the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the Law of Sines. In this case, side a is greater than the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the…

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate the centers of the holes B and C by finding the distance each is to the right and above the center O. The radius of the circle is 1.5 inches. Compute correct to three decimal places.

Circle With 36 degree Angles and Radius 1.5 in.

Circle with 36 degree angles marked. This diagram can be used with the following trig problem: Locate…

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height of the point P above the surface; it is required to find the distance from the point P to the horizon at A.

Circle With Center o and Radius r with point P

Circle modeling the earth. O is the center of the earth, r the radius of the earth, and h the height…

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of contact. The angle is measured by half the intercepted arc.

Circle With Chord and Tangent

Illustration of a circle showing an angle included by a tangent and a chord drawn from the point of…

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle AOB, and the central angle AOB has the same measure as the arc AnB.

Circle With a Chord of 2 ft. and a Radius of 3 ft.

Circle with chord AB=2 ft. and radius OA = 3 ft.. Triangle AOC is a right triangle. Angle AOC=half angle…

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Circle with Segment, Semicircle, Sector, Quadrant, and Central Angle

Illustrations of a circle with segment, semicircle, sector, quadrant, and central angles drawn.

Illustration of a circle with two intersecting chords within the circumference. The angle formed is measured by half the sum of the intercepted arcs.

Circle With Two Intersecting Chords

Illustration of a circle with two intersecting chords within the circumference. The angle formed is…

Illustration of a circle which illustrates that the tangents to a circle drawn from an external point are equal, and make equal angles with the line joining the point to the center.

Circle With Two Tangents Drawn From an External Point

Illustration of a circle which illustrates that the tangents to a circle drawn from an external point…

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to a circle form an external point. The angle is measured by half the difference of the intercepted arcs.

Circles With Angles Formed by Secants and Tangents

Illustration showing angles formed by two secants, two tangents, or a tangent and a secant, drawn to…