Question

16) PG RS is a parallelogram. If angle P=(2x +10°)
and angle R = (32-25°), find the value of x and
the measures of all angles of parellelogram PQRS​

Answer 1

Question:

PQRS is a parallelogram. If angle P=(2x +10)° and angle R = (3x-25)°, find the value of x and the measures of all angles of parellelogram PQRS.

Solution:

In parallelogram PQRS,

Angle P and Angle R are opposite.

Angle Q and Angle S are opposite.

In parallelogram, opposite angles are equal and sum of adjacent angles is 180°

Angle P = Angle R

(2x + 10)° = (3x - 25)°

3x° - 2x° = 25° + 10°

x° = 35°

Angle P + Angle Q = 180°

2(35°) + 10° + Angle Q = 180°

Angle Q = 100°

∴ Angle P = Angle R = 80°

Angle Q = Angle S = 100°