Today’s Lesson Determining Angle Measures when Parallel Lines Are Cut by a Transversal

How can you find the missing angle without using a protractor? 43° x x = 43° These angles are vertical. Vertical angles have the same angle measure.

The sum of the triangle’s angles equals 180 degrees. How can you find the missing angle of the triangle without using a protractor? 82° 32° x What do you know about triangles that will help you find the missing angle? The sum of the triangle’s angles equals 180 degrees.

The sum of the triangle’s angles equals 180 degrees. 82° 32° x 82 + 32 + x = 180 114 + x = 180 x = 180 – 114 x = 66 66°

Whole-Class Skills Lesson Today, you will focus on using patterns to find missing angles.

Congruent Angles 43° have the same measure in degrees

Parallel Lines Are always the same distance apart. They will never intersect.

Transversal A line that crosses a pair of parallel lines.

Corresponding Angles 1 2 4 3 A B D C Angles in the same position on parallel lines cut by a transversal are congruent.

Corresponding Angles 1 2 4 3 A B D C

Vertical angles have the same angle measure. The sum of the triangle’s angles equals 180 degrees. Supplementary angles add up to 180 degrees.

Lines a and b are parallel. c 1 2 3 4 5 7 8 6 What types of angles do you see in this example? Supplementary, Vertical, and Corresponding Angles

Lines a and b are parallel. c 1 2 3 4 5 7 8 6 Angles 1 and 5 Angles 4 and 8 Angles 2 and 6 Angles 3 and 7 Can you name the corresponding angles?

Lines a and b are parallel. c 1 2 3 4 5 7 8 6 Angles 1 and 3 Angles 4 and 2 Angles 5 and 7 Angles 6 and 8 Can you name the vertical angles?

Lines a and b are parallel. c 1 2 3 4 5 7 8 6 Angles 1 and 2 Angles 2 and 3 Angles 3 and 4 Angles 4 and 1 Angles 5 and 6 Angles 6 and 7 Can you name some of the supplementary angles? Angles 7 and 8 Angles 5 and 8

110° Lines a and b are parallel. c 110 2 3 4 5 7 8 6 If Angle 1 measures 110 degrees, what is the measure of Angle 3? 110°

70° Lines a and b are parallel. c 110 2 3 4 5 7 8 6 If Angle 1 measures 110 degrees, what is the measure of Angle 4? 70°

70° Lines a and b are parallel. c 110 2 3 4 5 7 8 6 If Angle 1 measures 110 degrees, what is the measure of Angle 8? 70°

110° Lines a and b are parallel. c 110 2 3 4 5 7 8 6 If Angle 1 measures 110 degrees, what is the measure of Angle 7? 110°

128° Lines a and b are parallel. c 1 2 3 4 5 7 8 52° If Angle 6 measures 52 degrees, what is the measure of Angle 7? 128°

Lines a and b are parallel. c 1 2 3 4 5 7 8 52° 128° 52° 52° 128° 128° 52° 128° If Angle 6 measures 52 degrees, what is the measure of all the angles on the diagram?