Answer:
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Explanation:
7.- The sum of the internal angles in a triangle equals 180°
2x + 22 + 4x + 11 + [180- (9x - 15)] = 180
6x + 180 - 9x + 15 = 180 - 33
-2x = 147 - 180 - 15
-2x = -48
x = -48/-3
x = 16
∠X = 2(16) + 22
∠X = 54° Letter D
8.-
8x - 31 + 6x - 8 + [180 - (10x + 17)] = 180
14x - 39 + 180 - 10x - 17 = 180
4x = 56
x = 56 / 4
x = 14
∠ ECD = 180 - 10(14) - 17
∠ECD = 180 - 140 - 17
∠ECD = 23° Letter C
9.-
ΔABC
m∠C = m∠A - 9
m∠B = 4m∠A - 15
The sum of the internal angles in a triangle equals 180°.
∠A + ∠B + ∠C = 180°
∠A + 4∠A - 15 + ∠A - 9 = 180
6∠A = 180 + 24
6∠A = 204
∠A = 204 / 6
∠A = 34
Then
∠B = 4∠A - 15
∠B = 4(34) - 15
∠B = 121 Letter B
10.-
∠XYZ = 2∠X - 9
m∠W = 38°
38 + ∠X + [180 - (2∠X - 9)] = 180
38 + ∠X + 180 - 2∠X + 9 = 180
-1∠X = -47
∠X = -47/-1
∠X = 47
Then,
∠XYZ = 2(47) - 9
∠XYZ = 85° Letter E