MATHEMATICS

JAMB 2000 - Question 29

Mathematics 2000 JAMB Past Questions - Question 29: In the diagram above, if ∠RPS = 50°, ∠RPQ = 30° and PQ = QR, find the value of ∠PRS.

In the diagram above, if ∠RPS = 50°, ∠RPQ = 30° and PQ = QR, find the value of ∠PRS.
In the diagram above, if ∠RPS = 50°, ∠RPQ = 30° and PQ = QR, find the value of ∠PRS.
A:
B:
C:
D:
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Correct Answer

B

Explanation

To find the value of ∠PRS, we can use the properties of angles in a triangle.In triangle PQR, we know that PQ = QR, which means that the triangle is isosceles. Therefore, the angles ∠PQR and ∠QPR are equal.Since ∠RPQ = 30°, and ∠PQR = ∠QPR, we can find ∠PQR by subtracting the given angles from 180°:∠PQR = 180° - ∠RPQ - ∠RQP∠PQR = 180° - 30° - 50°∠PQR = 100°Since ∠PQR = ∠QPR, we can conclude that ∠QPR is also 100°.Now, to find ∠PRS, we can use the fact that the angles in a triangle add up to 180°:∠PRS = 180â�° - ∠RPS - ∠QPR∠PRS = 180° - 50° - 100°∠PRS = 30°Therefore, the value of ∠PRS is 30°.