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Question
In ΔPQR, PR = QR. ∠P = 2x – 10°, ∠R = x + 5°.
∴ The value of x is ______.
Options
45°
39°
40°
42°
MCQ
Fill in the Blanks
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Solution
∴ The value of x is 39°.
Explanation:
1. Given:
PR = QR triangle is isosceles with equal sides PR and QR.
Therefore, ∠P = ∠Q.
∠P = 2x – 10°
∠R = x + 5°
2. Since PR = QR, the angles opposite them are equal:
So, ∠P = ∠Q
= 2x – 10°
3. Using the angle sum property of triangle:
∠P + ∠Q + ∠R = 180°
Substitute values:
(2x – 10) + (2x – 10) + (x + 5) = 180°
4x – 20 + x + 5 = 180°
5x – 15 = 180°
5x = 195°
x = 39°
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