Answer:
angle 6 = 5x - 10, angle 3 = 8x - 34
angle 6 = angle 3
5x - 10 = 8x - 34
-10 + 34 = 8x - 5x
24 = 3x
24/3 = 3x/3
8 = x
angle 6 = 5x - 10
= 5(8) - 10
= 40 - 10
angle 6 = 30°
angle 3 = 8x - 34
= 8(8) - 34
= 64 - 34
angle 3 = 30°
angle 1: angle 3 + angle 1 = 180°
: 30° + angle 1 = 180°
: angle 1 = 180° - 30 °
: angle 1 = 150°
angle 2: angle 1 + angle 2 = 180°
: 150° + angle 2 = 180°
: angle 2 = 180° - 150°
angle 2 = 30°
angle 2 = angle 3
angle 4: angle 2 + angle 4 = 180°
: 30° + angle 4 = 180°
: angle 4 = 180° - 30°
: angle 4 = 150°
angle 4 = angle 1
angle 5: angle 6 + angle 5 = 180°
: 30° + angle 5 = 190°
: angle 5 = 180° - 30°
: angle 5 = 150°
angle 7: angle 7 + angle 5 = 180°
: angle 7 + 150° = 180°
: angle 7 = 180° - 150°
: angle 7 = 30°
angle 7 = angle 6
angle 8: angle 8 + angle 7 = 180°
: angle 8 + 30° = 180°
: angle 8 = 180° - 30°
: angle 8 = 150°
angle 8 = angle 5