When two lines intersect, they form four angles around the point of intersection. These angles are formed in such a way that opposite angles (also called vertical angles) are equal. Given that the angles are labeled A, B, C, and D, with B being adjacent to both A and C, we can use the properties of angles to find the measure of ∠A.
Since ∠B is adjacent to both ∠A and ∠C, it means that ∠B forms a linear pair with these angles. A linear pair of angles are two adjacent angles whose non-common sides form a straight line, which means they add up to 180 degrees.
From the problem, we know:
- m∠C = 75°
- Because vertical angles are equal, the angle opposite ∠C would also be 75° (this would be ∠A).
Thus, the measure of ∠A is the same as the measure of ∠C:
- m∠A = 75°
The correct response is:
75 degrees
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°.(1 point)
Responses
180°
180 degrees
15°
15 degrees
105°
105 degrees
75°
1 answer