Question

1(a) In a triangle PQR, angle Q is three-quarter of angle P and angle R is half of angle P. If the measure of angle P is (x + 5)°, form an equation in x and hence calculate the angles of triangle PQR.

Accepted Answer

Angle P = (x + 5)°
Angle Q = 3/4 (x + 5)°
Angle R = 1/2 (x + 5)°

Angles of a triangle add up to 180°:
(x + 5) + 3/4 (x + 5) + 1/2 (x + 5) = 180
Multiply through by 4: 4(x + 5) + 3(x + 5) + 2(x + 5) = 720
9(x + 5) = 720
x + 5 = 80, so x = 75

Angle P = 80°
Angle Q = 3/4 × 80 = 60°
Angle R = 1/2 × 80 = 40°
Check: 80 + 60 + 40 = 180°

JSCE Mathematics 2022 Theory — Question 1

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