Question

In the following figures, find the remaining angles of the  parallelogram

Answer 1

PQRS is a parallelogram.
∠R + ∠Q = 180°    ....(Interior angles)

⇒ `x° +  (x°)/(4)` = 180°

⇒ 4x° + x° = 180° x 4
⇒ 5x° = 180° x 4

⇒ x° = `(180° xx 4)/(5)`

⇒ x° = 144° = ∠R

⇒ `x°/(4) = (144°)/(4)` = 36° = ∠Q

⇒ ∠P = ∠R = 144    ....(Opposite angles of a parallelogram are equal)
∠S = ∠Q = 36°.