1. 9.1
Angle Relationships
How can you use angle relationships to solve problems?

2. Texas Essential Knowledge and Skills
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.

3. ADDITIONAL EXAMPLE 1 Use the diagram. A
Name a pair of vertical angles.
AEC and BED B
Name a pair of adjacent angles.
Sample answer: BEF and AEF

4. ADDITIONAL EXAMPLE 1 Use the diagram. C
Name a pair of complementary angles.
BEF and BED D
Name a pair of supplementary angles.
Sample answer: AEF and BEF

5. ADDITIONAL EXAMPLE 2 A Find the measure of RST. m RST = 144° B
Find the measure of HJK.
m HJK = 40°

6. ADDITIONAL EXAMPLE 3
One 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 of
each of the base angles.
25°

7. 9.1 LESSON QUIZ 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.

8. For Exercises 1–3, use the figure.2.
Name a pair of complementary angles.
Sample answer: RUS and SUT 3.
Find m VUR. Justify your answer.
130°; VUR and RUS are supplementary, so their sum is 180°. 130° + 50° = 180°.

9. 4.
Find the value of x and m HKL.
x = 25; m HKL = 102°

10. For Exercises 5 and 6, use the figure.5.
m VUW
50° 6.
m TUW
90°

11. Word Search: Find each of the words from this lesson.
adjacent
angle
base
complementary
congruent
isosceles
sum
supplementary
triangle
vertical

12. 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.