An angle measures 30° more than the measure of its supplementary angle. What is the measure of each angle?
1 answer:
Hi there!
Let there be two angles, ∠A and ∠B, that are supplementary to each other. Therefore:
∠A + ∠B = 180°
We can assign ∠B to be the greater angle. Assume ∠A has a measure of x°.
∠A = x°
∠B = x° + 30°
The sum is equal to 180°, so:
x° + (x° + 30°) = 180°
Solve for x°.
2x° + 30° = 180°
2x° = 150°
x° = 75°
Thus, ∠A = 75°.
Since ∠B is 30°, greater:
∠B = 75° + 30° = 105°.
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