Question

In a parallelogram PQRS, measure of angle P and angle Q are in the ratio 2:3. Find the measure of angle P?

Answer 1

All the angles of quadrilateral are 84°,96°,84° and 96°

Step-by-step explanation:

assume that the ratio of p:q = 7:8

In parallelogram sum of consecutive angles is 180°

In PQRS

let the ratio be x

then

7x+8x = 1807x+8x=180

15x = 18015x=180

x= \frac{180}{15}x=

15

180

x= 12

so the angles are

7x = 7×12 = 84°

8x = 8× 12 = 96°

since , In parallelogram opposite angles are equal then

\angle P = 84∠P=84 °

\angle Q = 96∠Q=96 °

\angle R = 84∠R=84 °

\angle S = 96∠S=96 °

hence , all the angles of quadrilateral are 84°,96°,84° and 96°

to check :

sum of all the angles of a quadrilateral is 360°