Madhya Pradesh Police Exam Model Paper 3

Given: ABCD is a parallelogram The ratio of adjacent angles = 4 ∶ 5 Concept used: The Sum of adjacent angles of the parallelogram is 180°. The opposite angles of the parallelogram are always equal to each other. Calculation:ABCD is a parallelogram, Let the ∠A and ∠D be 4x and 5x respectively. $\angle A + \angle D = 180^{\circ}$ [Adjacent angles of parallelogram] $\Rightarrow 4x + 5x = 180^{\circ}$ $\Rightarrow 9x = 180^{\circ}$ $\Rightarrow x = 20^{\circ}$ $\angle A = 4x$ $\Rightarrow \angle A = 4 \times 20^{\circ}$ $\Rightarrow \angle A = 80^{\circ}$ $\angle D = 5x$ $\Rightarrow \angle D = 5 \times 20^{\circ}$ $\Rightarrow \angle D = 100^{\circ}$ ∠A = ∠C [Opposite angle of parallelogram] ∠D = ∠B [Opposite angle of parallelogram] So, $\angle A = \angle C = 80^{\circ}$ $\angle D = \angle B = 100^{\circ}$ ∴ All angles of parallelogram is 80°, 100°, 80°, 100°.