Question

Given:

Answer 1

<7 = <5   vertical angles

<5 = <3  alternate interior angles are equal when the lines are parallel

<2 +<3 = 180  straight line  ( complementary angles)

3x+20 + <3 = 180

subtract 3x+20 from each side

<3 = 180 -(3x+20)

<3 = 180 -3x-20

<3 =160 -3x

but from above

<3 also = <5 = <7  and <7 = 2x-10

160 - 3x = 2x-10

add 3x to each side

160 = 5x-10

add 10 to each side

170 = 5x

x = 34

substitute in x=34 to find angle 3

<3 = 160 -3x

<3 =160 -3(34)

<3 =58

to find angle 6

<7+<6 = 180

<7 =<3 = 58

58 + <6 = 180

subtract 58 from each side

<6 = 180 -58

<6 = 122