Question

In the adjoining figure, PQRS and ABCR are two parallelograms. If ∠P = 110°, then find the measures of all the angles of ABCR.

Answer 1

PQRS is a parallelogram. [Given] 

∴ ∠R = ∠P [Opposite angles of a parallelogram] 

∴ ∠R = 110° …..(iii) 

ABCR is a parallelogram. [Given] 

∴ ∠A + ∠R= 180° [Adjacent angles of a parallelogram are supplementary] 

∴ ∠A + 110°= 180° [From (i)] 

∴ ∠A = 180°- 110° 

∴ ∠A = 70° 

∴ ∠C = ∠A = 70° 

∴ ∠B = ∠R= 110° [Opposite angles of a parallelogram]

∴ ∠A = 70°, ∠B = 110°, 

∴ ∠C = 70°, ∠R = 110°