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Course: Praxis Core Math > Unit 1

Lesson 5: Geometry
Test prep
Praxis Core Math
Lessons
Geometry
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Angles | Lesson

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What are angles?

An angle is formed by two lines, line segments, or rays diverging from a
.
Angles are measured in 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 x∘ and y∘ are supplementary angles. Usually seen on the same side of an intersection of two lines, the measures of supplementary angles add up to 180∘: x∘+y∘=180∘.
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 x∘ and another measuring y∘.

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, ℓ1 and ℓ2 are parallel, and ℓ3 is a transversal. The angles at the intersection of ℓ1 and ℓ3 have the same measures and are in the same arrangement as the angles at the intersection of ℓ2 and ℓ3.

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∘:
x∘+y∘+z∘=180∘

Your turn!

TRY: IDENTIFYING VERTICAL ANGLES
What is the value of x in the figure above?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

TRY: PARALLEL LINES AND TRANSVERSAL
In the figure above, l and m are parallel lines. What is the value of x ?
Choose 1 answer:

TRY: MIXED ANGLES PROPERTIES
In the figure above, ℓ1 and ℓ2 are not parallel. Which of the following statements are true?
Choose all answers that apply:

TRY: INTERIOR ANGLES
Triangle ABC is shown in the figure above. What is the measure, in degrees, of angle B ?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
degrees

Things to remember

The measures of supplementary angles add up to 180∘.
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∘, y∘, and z∘:
x∘+y∘+z∘=180∘

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