PQRS is a cyclic quadrilateral If angle P is three times the angle R and angle S is five times the a...........

Quantitative Aptitude (CGL) Geometry

PQRS is a cyclic quadrilateral. If angle P is three times the angle R and angle S is five times the angle Q,then the sum of the

angles Q and R is:

This questions was previously asked in

SSC CGL 6 June 2019 Shift-3

65^o

75^o

72^o

70^o

- In a cyclic quadrilateral, opposite angles are supplementary.

- Angle P + Angle R = 180°.

- Angle Q + Angle S = 180°.

- Given: Angle P = 3 * Angle R, Angle S = 5 * Angle Q.

- Substitute the given values:

- Angle P = 3R

- Angle S = 5Q

- Equation for P and R: 3R + R = 180° ? 4R = 180° ? R = 45°.

- Equation for Q and S: Q + 5Q = 180° ? 6Q = 180° ? Q = 30°.

- Sum of angles Q and R is Q + R = 30° + 45° = 75°.

Correct Answer: Option: 2, 75°

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