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. Standards California 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. 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°
So m1 = m3, or 1  3.

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

6. 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)
= 180° – 180° + y°
Distributive Property
= y°
Simplify.
So m4 = m2, or 4  2.

7. Use the diagram to find each angle measure.
Check It Out! Example 1
Use the diagram to find each angle measure. 1 2 3 4
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°
So m1 = m3, or 1  3.

8. Use the diagram to find each angle measure.
Check It Out! Example 1
Use the diagram to find each angle measure. 1 2 3 4
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)
= 180° – 180° + x°
Distributive Property
= x°
Simplify.
So m4 = m2, or 4  2.

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. 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 ° = 180°
–124° –124°
Subtract.
m = 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.
C. 6
2 and 6 are corresponding angles.
m6 = 56°

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

16. 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 ° = 180° 1
144° 3 4 5 6 7 8 m n
–144° –144°
m = 36°

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