Two intersecting lines create four angles with the same vertex, labeled A, B, C, and D. Angle B is adjacent to ∠A and ∠C. Find m∠A if m∠C=75°
m∠A = 75°
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To find the measure of angle A, we know that angle B is adjacent to both angle A and angle C. This means that the sum of angle A and angle B should be equal to the sum of angle B and angle C.
Let's represent the measure of angle A as 'x':
The sum of angles A and B: A + B
The sum of angles B and C: B + C
We are given that angle C is 75°. Therefore:
Sum of angles B and C: B + C = B + 75°
According to the information given, the sum of angles A and B should be equal to the sum of angles B and C:
A + B = B + C
Since C = 75°, we can substitute it into the equation:
A + B = B + 75°
Now, solve for A:
A = B + 75° - B
A = 75°
So, the measure of angle A is 75°.