Question

Two angles in triangle PQR are congruent, ∠P and ∠Q; ∠R measures 28.45°. What is the measure of ∠P?


a) 28.45°

b) 75.775°

c) 121.55°

d) 151.55°

Answer 1

Since triangle PQR is a triangle, the sum of all the angles is 180°.

Let's assume that the measure of ∠P and ∠Q is x.
Therefore, the sum of ∠P, ∠Q, and ∠R is x + x + 28.45° = 2x + 28.45°.

Since the sum of all the angles in a triangle is 180°, we can set up the equation:
2x + 28.45° = 180°.

Now, subtract 28.45° from both sides:
2x + 28.45° - 28.45° = 180° - 28.45°,
2x = 151.55°.

Finally, solve for x by dividing both sides by 2:
2x / 2 = 151.55° / 2,
x = 75.775°.

So, the measure of ∠P is 75.775°.

Answer: b) 75.775°.