Lesson 4 Lines & Angles Vertical Angles

Warm-Up N and M are complementary. The measure of M is 83º. Find the measure of N. Find the value of x. Write the angle measures of a pair of supplementary angles. How do you know your angle measures are supplementary?

Target: Understand and apply the properties of vertical angles.

Vocabulary Vertical Angles: Nonadjacent angles formed by two intersecting lines. Linear Pair: Two adjacent angles whose non-common sides are opposite rays.

Angle Relationships Vertical angles are equal in measure. If two angles form a linear pair, they are supplementary angles.

Example 1 Find the measure of each missing angle. a. m3 Vertical angles are congruent. m2 = m3 54° = m3 b. m1 m1 and m2 are a linear pair. m1 + m2 = 180 Substitute known values. m1 + 54 = 180 Subtract 54 from each side. –54 –54 m1 = 126° c. m4 Vertical angles are congruent. m1 = m4 126° = m4

Example 2 Use the diagram to the right. a. Solve for x. b. Find the measure of each angle. a. Vertical angles have equal measures. 3x + 7 = x + 30 Subtract x from each side. –x –x 2x + 7 = 30 Subtract 7 from each side. –7 –7 2x = 23 Divide by 2 on each side. 2 2 x = 11.5 b. Substitute the solution for x in each angle expression. (3x + 7) = (3(11.5) + 7) = (34.5 + 7) = 41.5° (x + 30) = (11.5 + 30) = 41.5° The measure of each angle is 41.5°.

Exit Problems Find the value of x.

Communication Prompt Why do you think equation-solving is one of the most important mathematical skills?