Angles Warm-Up: Solving Problems with Complementary and Supplementary Angles

1. Preview Warm Up California Standards Lesson Presentation

2. Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . 2. A part of a line that starts at one point and extends forever in one direction is called a _______. 3. Angles whose measures have a sum of 180° are ______________. 4. A part of a line between two points is called a ____________. complementary ray supplementary segment

3. California Standards Review of Grade 6 MG2.2 Use properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Also covered: 6MG2.1

4. So m1 = m3, or 1 3. Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. A. If m1 = 37°, find m3. 1 and 2 are supplementary. m2 = 180° – 37° = 143° The measures of 2 and 3 are supplementary. m3 = 180° – 143° = 37°

5. Writing Math ~ The symbol for congruence is =, which is read as “is congruent to.”

6. So m4 = m2, or 4 2. Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. B. If m4 = y°, find m2. 3 and 4 are supplementary. m3 = 180° – y° 2 and 3 are supplementary. m2 = 180° – m3 Substitute 180o – yo for m3. = 180° – (180o – yo) Distributive Property = 180° – 180° + y° = y° Simplify.

7. 3 2 4 1 So m1 = m3, or 1 3. Check It Out! Example 1 Use the diagram to find each angle measure. A. If m1 = 42°, find m3. The measures of 1 and 2 are supplementary. m2 = 180° – 42° = 138° The measures of 2 and 3 are supplementary. m3 = 180° – 138° = 42°

8. 3 2 4 1 So m4 = m2, or 4 2. Check It Out! Example 1 Use the diagram to find each angle measure. B. If m4 = x°, find m2. 3 and 4 are supplementary. m3 = 180° – x° 2 and 3 are supplementary. m2 = 180° – m3 Substitute 180o – xo for m3. = 180° – (180o – xo) Distributive Property = 180° – 180° + x° = x° Simplify.

9. The angles in Example 1 are examples of adjacent angles and vertical angles. These angles have special relationships because of their positions. Adjacent angles have a common vertex and a common side, but no common interior points. Vertical angles are the nonadjacent angles formed by two intersecting lines.

10. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angle pairs with special properties.

12. Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. A. 4 Corresponding angles are congruent. m4 = 124°

13. –124° –124° Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. B. 2 2 is supplementary to the 124° angle. m2 + 124° = 180° Subtract. m2 = 56° Simplify.

14. Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of the angle. 2 and 6 are corresponding angles. C. 6 m6 = 56°

15. 144° 1 m 4 3 6 5 n 8 7 Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. Alternate exterior angles are congruent. A. 7 m7 = 144°

16. 144° 1 m 4 3 6 5 n 8 7 –144° –144° Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. B. 1 1 is supplementary to the 144° angle. m1 + 144° = 180° m1 = 36°

17. 144° 1 m 4 3 6 5 n 8 7 Check It Out! Example 2 In the figure, line l|| line m. Find the measure of the angle. C. 6 Corresponding angles are congruent. m6 = 144°

18. Lesson Quiz In the figure, line a || line b. 1. Name all angles congruent to 3. 1, 5, 7 2. Name all the angles supplementary to 6. 1, 3, 5, 7 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60°