Question

Find the angle measures. Justify your responses.

Answer 1

Answer:

m∠3 = 2x - 10° and m∠6 = 3x + 20

m∠3 = 58°          ;    m ∠6 = 122°

Step-by-step explanation:

a ║ b

m∠2 = m∠6                     If ║ cut by a transversal, then corresponding angles

                                         are ≅ and =

m∠7 = m∠3                   If ║ cut by a transversal, then corresponding angles

                                       are ≅ and =

m∠2 = 3x + 20              Given

m∠7 = 2x - 10                 Given    

m∠6 + m∠3 = 180°         If ║ cut by a transversal, then each pair of same-side

                                       interior angles (also called consecutive interior angles

                                       are supplementary (sum = 180°) .    

3x + 20 + 2x - 10 = 180°

5x + 10 = 180°

5x = 170°

x = 34°

Answer:   m∠3 = 2x - 10° and m∠6 = 3x + 20

                m∠3 = 2(34) - 10  ;    m∠6 = 3(34) + 20

                 m∠3 = 58°          ;    m ∠6 = 122°