Question

Please help me solve these problems

Answer 1

Will do first question of each concept only because the rest of the questions are the same concept (the same few repeat but whatever).

1. Total angle = (n - 2) * 180 --> 4 * 180 = 360°

70 + 130 + 120 + θ = 360 --> 320 + θ = 360 --> θ = 40

4. Total angle = (10 - 2) * 180 --> 8 * 180 = 1440

1440/10 = 144°

6. Interior: (n - 2) * 180 --> 10 * 180 = 1800

Exterior: 12 * 180 = 2160 --> 2160 - 1800 = 360

9. (n - 2) * 180 --> 3 * 180 = 540

90 + 90 + 150 + 160 + θ = 540 --> 490 + θ = 540 --> θ = 50

13. Interior: (n - 2) * 180 --> 2 * 180 = 360

Exterior: n * 180 - (n - 2) * 180 --> 180n - 180n + 360 --> 360 (always the same)

16. 7r + 4r + 8r + 5r = 360 --> 24r = 360 --> r = 15