two intersecting lines create four angles with the same vertex, labeled A, B, C, and D. Angle B is adjacent to angle A and angle C. Find m-angle A if m-angle C = 75°
Answers that are given:
A. 180°
B. 15°
C. 75°
D. 105°
To find the measure of angle A, we can use the fact that the sum of angles around a point is equal to 360 degrees.
m(A) + m(B) + m(C) + m(D) = 360°
Given that m(C) = 75°, we can plug this into the equation:
m(A) + m(B) + 75° + m(D) = 360°
We also know that angle B is adjacent to angle A and angle C, so the sum of angles A, B, and C is 180°.
m(A) + m(B) + 75° = 180°
Substitute this equation into the previous one:
180° + m(D) = 360°
Now solve for m(D):
m(D) = 360° - 180° = 180°
Since angle D is opposite angle A, angle A is equal to angle D:
m(A) = m(D) = 180°
Therefore, the measure of angle A is 180°. So the correct answer is:
A. 180°