Given: m∠RPQ = 23°; m∠TPR = 85°

Question

If ∠SPR and ∠RPQ are complementary angles, then what is the measure of ∠TPS?
A. 67°
B. 18°
C. 5°
D. 23°

Answer 1

Since ∠SPR and ∠RPQ are complementary angles, we know that:

m∠SPR + m∠RPQ = 90°

Let's call the measure of ∠SPR x. Then we can set up the equation:

x + 23° = 90°

Subtracting 23° from both sides, we get:

x = 67°

Now we need to find the measure of ∠TPS. We know that:

m∠TPR + m∠RPS + m∠SPQ = 180°

Substituting in the values we know, we get:

85° + m∠RPS + 67° = 180°

Simplifying, we get:

m∠RPS = 28°

Now we can find the measure of ∠TPS by using the fact that the angles in a triangle add up to 180°:

m∠TPS = 180° - m∠TPR - m∠RPS

Substituting in the values we know, we get:

m∠TPS = 180° - 85° - 28°

Simplifying, we get:

m∠TPS = 67°

Therefore, the answer is A. 67°.