LESSON

How can you use angle relationships to solve problems?

Angle Relationships9.1

The student is expected to:

Expressions, equations, and relationships—7.11.C

Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.

Mathematical Processes

7.1.D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Texas Essential Knowledge and Skills

ADDITIONAL EXAMPLE 1

A Name a pair of vertical angles.

B Name a pair of adjacent angles. AEC and BED

Sample answer: BEF and AEF

Use the diagram.

ADDITIONAL EXAMPLE 1

C Name a pair of complementary angles.

D Name a pair of supplementary angles. BEF and BED

Sample answer: AEF and BEF

Use the diagram.

ADDITIONAL EXAMPLE 2A Find the measure of RST. m RST = 144°

B Find the measure of HJK. m HJK = 40°

ADDITIONAL EXAMPLE 3One side of the roof of a doghouse is shaped like an isosceles triangle. The measure of the angle at the top of the triangle is 130°. Find the measure ofeach of the base angles. 25°

9.1 LESSON QUIZ7.11.C

For Exercises 1–3, use the figure.

1. Name a pair of adjacent angles. Explain why they are adjacent.Sample answer: RUV and RUS are adjacent angles because they share a vertex and one side and do not overlap.

2. Name a pair of complementary angles.

Sample answer: RUS and SUT

3.

130°; VUR and RUS are supplementary, so their sum is 180°. 130° + 50° = 180°.

Find m VUR. Justify your answer.

For Exercises 1–3, use the figure.

4.

x = 25; m HKL = 102°

Find the value of x and m HKL.

For Exercises 5 and 6, use the figure.

5. 50°m VUW

6. 90°m TUW

Word Search: Find each of the words from this lesson.adjacentanglebasecomplementarycongruentisoscelessumsupplementarytrianglevertical

How can you use angle relationships to solve problems?

Sample answer:You can use the relationships about angle pairs, such as supplementary, complementary, or vertical angles, to write and solve an equation to find the unknown measure of an angle.