The unknown angles are as follows:
- x = 29
- z = 13
- ∠RIG = 59°
- ∠ZIM = 149°
How to find angles when line intersect?
∠AIM is perpendicular to IR.
Therefore,
∠RIM = 90°
Line AM, ZG and RI intersect at point I.
Therefore,
3x - 56 = x + 2 (vertically opposite angles)
3x - x = 2 + 56
2x = 58
x = 58 / 2
x = 29
4z + 7 + x + 2 = 90
4z + 7 + 29 + 2 = 90
4z = 90 - 7 - 2 - 29
4z = 52
z = 52 / 4
z = 13
∠RIG = 4z + 7
∠RIG = 4(13) + 7
∠RIG = 52 + 7
∠RIG = 59°
∠ZIM = 4z + 7 + 90
∠ZIM = 4(13) + 7 + 90
∠ZIM = 52 + 7 + 90
∠ZIM = 59 + 90
∠ZIM = 149 degrees
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