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# Angles | Lesson

## What are angles?

An angle is formed by two lines, line segments, or rays diverging from a
vertex
.
Angles are measured in degrees (degrees), which describe how spread apart intersecting lines or line segments are. Narrow spreads have small angle measures, while wide spreads have large angle measures.

### What skills are tested?

• Recognizing supplementary and vertical angles
• Recognizing identical angles formed by two parallel lines and a transversal
• Calculating angle measures using our knowledge of angle relationships
• Calculating the measures of interior angles of polygons

## What are supplementary and vertical angles?

In the figure below, the angles measuring start color #11accd, x, degrees, end color #11accd and start color #ca337c, y, degrees, end color #ca337c are supplementary angles. Usually seen on the same side of an intersection of two lines, the measures of supplementary angles add up to 180, degrees: start color #11accd, x, degrees, end color #11accd, plus, start color #ca337c, y, degrees, end color #ca337c, equals, 180, degrees.
The angles on the opposite sides of an intersection of two lines are vertical angles. They have the same measure. The figure above shows two sets of vertical angles, one measuring start color #11accd, x, degrees, end color #11accd and another measuring start color #ca337c, y, degrees, end color #ca337c.

## How are angles formed by parallel lines and transversals related?

A
transversal
of two
parallel lines
creates two sets angles with identical angle measures at the intersections. In the figure below, ell, start subscript, 1, end subscript and ell, start subscript, 2, end subscript are parallel, and ell, start subscript, 3, end subscript is a transversal. The angles at the intersection of ell, start subscript, 1, end subscript and ell, start subscript, 3, end subscript have the same measures and are in the same arrangement as the angles at the intersection of ell, start subscript, 2, end subscript and ell, start subscript, 3, end subscript.

## How are the interior angles of polygons related?

A triangle has three
interior angles
. The measures of the three interior angles in a triangle add up to 180, degrees:
start color #11accd, x, degrees, end color #11accd, plus, start color #ca337c, y, degrees, end color #ca337c, plus, start color #1fab54, z, degrees, end color #1fab54, equals, 180, degrees

TRY: IDENTIFYING VERTICAL ANGLES
What is the value of x in the figure above?

TRY: PARALLEL LINES AND TRANSVERSAL
In the figure above, l and m are parallel lines. What is the value of x ?

TRY: MIXED ANGLES PROPERTIES
In the figure above, ell, start subscript, 1, end subscript and ell, start subscript, 2, end subscript are not parallel. Which of the following statements are true?

TRY: INTERIOR ANGLES
Triangle A, B, C is shown in the figure above. What is the measure, in degrees, of angle B ?
degrees

## Things to remember

The measures of supplementary angles add up to 180, degrees.
Vertical angles have the same measure.
A transversal of two parallel lines creates two identical sets of angles at each intersection.
In a triangle with angle measures x, degrees, y, degrees, and z, degrees:
x, degrees, plus, y, degrees, plus, z, degrees, equals, 180, degrees