01/23/17 Warm Up 2.4 On Desk Do the Daily Quiz 2.3

ESSENTIAL OBJECTIVE Calculate Angle Measures of Angles formed by Intersecting Lines

VOCABULARY Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

Linear Pair: Two adjacent angles whose opposite rays form a straight line.

Linear Pair: Two adjacent angles whose opposite rays form a straight line.

Determine whether the labeled angles are vertical angles, Example 1 Identify Vertical Angles and Linear Pairs Determine whether the labeled angles are vertical angles, a linear pair, or neither. b. a. c. SOLUTION a. 1 and 2 are a linear pair. b. 3 and 4 are neither. c. 5 and 6 are vertical angles 8

Linear Pair Postulate: If two angles form a linear pair, then they are supplementary

Find the measure of RSU. Example 2 Use the Linear Pair Postulate Find the measure of RSU. SOLUTION RSU and UST are supplementary. To find mRSU, subtract mUST from 180°. mRSU = 180° – mUST = 180° – 62° = 118° 10

Vertical Angles Theorem Vertical Angles are Congruent (  )

Vertical Angles Theorem Vertical Angles are Congruent (  )

Find the measure of CED. Example 3 Use the Vertical Angles Theorem Find the measure of CED. SOLUTION AEB and CED are vertical angles. CED  AEB, so mCED = mAEB = 50°. 13

Example 4 Find m1, m2, and m3. SOLUTION m2 = 35° Find Angle Measures Find m1, m2, and m3. SOLUTION m2 = 35° m1 = 180° – 35° = 145° m3 = m1 = 145° 14

Checkpoint Find m1, m2, and m3. 1. Find Angle Measures Find m1, m2, and m3. 1. ANSWER m1 = 152°; m2 = 28°; m3 = 152° 2. ANSWER m1 = 56°; m2 = 124°; m3 = 56° 3. ANSWER m1 = 113°; m2 = 67°; m3 = 113°

Find the value of the variable. 4. ANSWER 43 Checkpoint Use Algebra with Angle Measures Find the value of the variable. 4. ANSWER 43 5. ANSWER 16 6. ANSWER 5

Algebraic expressions are measures of vertical Example 5 Use Algebra with Vertical Angles Find the value of y. SOLUTION Algebraic expressions are measures of vertical angles, you can write the following equation. (4y – 42)° = 2y° 4y – 42 – 4y = 2y – 4y –42 = –2y –2 –42 –2y = 21 = y . 17

Review

Determine whether the angles are complementary, supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1. 2.

Determine whether the angles are complementary, supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1. ANSWER complementary; adjacent 2. ANSWER neither; nonadjacent

Find the measures of a complement and a supplement of the angle. 3. mR = 27° 4. mT = 11° 5. In the figure at the right, ABD and DBC are complementary angles. Find the value of x.

Find the measures of a complement and a supplement of the angle. 3. mR = 27° ANSWER 63°; 153° 4. mT = 11° ANSWER 79°; 169° 5. In the figure at the right, ABD and DBC are complementary angles. Find the value of x. ANSWER x = 7

Hw Worksheet 2.4 B