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### Course: Praxis Core Math > Unit 1

Lesson 5: Geometry- Properties of shapes | Lesson
- Properties of shapes | Worked example
- Angles | Lesson
- Angles | Worked example
- Congruence and similarity | Lesson
- Congruence and similarity | Worked example
- Circles | Lesson
- Circles | Worked example
- Perimeter, area, and volume | Lesson
- Perimeter, area, and volume | Worked example

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# Angles | Lesson

## What are angles?

An

**angle**is formed by two lines, line segments, or rays diverging from a .Angles are measured in degrees (${}^{\circ}$ ), 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 ${{x}^{\circ}}$ and ${{y}^{\circ}}$ are ${180}^{\circ}$ : ${{x}^{\circ}}+{{y}^{\circ}}={180}^{\circ}$ .

**supplementary angles**. Usually seen on the same side of an intersection of two lines, the measures of supplementary angles add up toThe angles on the opposite sides of an intersection of two lines are ${{x}^{\circ}}$ and another measuring ${{y}^{\circ}}$ .

**vertical angles**. They have the same measure. The figure above shows two sets of vertical angles, one measuring## How are angles formed by parallel lines and transversals related?

A of two creates two sets angles with identical angle measures at the intersections. In the figure below, ${\ell}_{1}$ and ${\ell}_{2}$ are parallel, and ${\ell}_{3}$ is a transversal. The angles at the intersection of ${\ell}_{1}$ and ${\ell}_{3}$ have the same measures and are in the same arrangement as the angles at the intersection of ${\ell}_{2}$ and ${\ell}_{3}$ .

## How are the interior angles of polygons related?

A triangle has three . The measures of the three interior angles in a triangle add up to ${180}^{\circ}$ :

## Your turn!

## Things to remember

The measures of supplementary angles add up to ${180}^{\circ}$ .

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 ${x}^{\circ}$ , ${y}^{\circ}$ , and ${z}^{\circ}$ :

## Want to join the conversation?

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