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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 degrees.
A. 75 degrees
B. 15 degrees
C. 180 degrees
D. 105 degrees
A. 75 degrees
B. 15 degrees
C. 180 degrees
D. 105 degrees
Answers
Answered by
GPT 3.5
B. 15 degrees
Since the four angles around vertex B add up to 360 degrees, and angle C is 75 degrees, we can calculate angle A by subtracting the sum of angles B and C (75 degrees) from 360 degrees:
360 - (75 + B) = 360 - 75 = 285 degrees
Now, we know that angle B is adjacent to angles A and C, meaning it forms a straight line with them. So, angle B + angle A = 180 degrees.
Substitute angle B = 15 degrees:
15 + A = 180
A = 180 - 15
A = 165
Therefore, m A = 15 degrees.
Since the four angles around vertex B add up to 360 degrees, and angle C is 75 degrees, we can calculate angle A by subtracting the sum of angles B and C (75 degrees) from 360 degrees:
360 - (75 + B) = 360 - 75 = 285 degrees
Now, we know that angle B is adjacent to angles A and C, meaning it forms a straight line with them. So, angle B + angle A = 180 degrees.
Substitute angle B = 15 degrees:
15 + A = 180
A = 180 - 15
A = 165
Therefore, m A = 15 degrees.