Question

In a parallelogram PQRS . If angle P=(2x-40°),angle Q=(y+15°) , angle R=(x+30°).Then find the value of x and y .​

Answer 1

Answer:

Answer

We know that, opposite angles of a parallelogram are equal.

... ZQ = ZS

→ 4x 5 = 3x + 10

+ 4x

- 3x

+ x= 15

=

10+5

+ ZQ = (4x - 5)º = (4 x 15 - 5)° = 55°

We know that, sum of adjacent angles of parallelogram is 180°

> ZQ + ZR= 180°

> 55° + ZR = 180°

.. ZR = 125°

Answer 2

Answer:

Angles suspended by the opposite vertices in parallelogram are equal.

So,  ∠P=∠R  and  ∠Q=∠S  ------(1)

And sum of angles of a parallelogram is 360

So,  ∠P+∠Q+∠R+∠S=360  ———-(2)

So, for the parallelogram PQRS

=>2(∠P+∠Q)=360  

=>∠P+∠Q=180  ———-(3)

As,  ∠P=4×∠Q  (Given) ————-(4)

So, equation  (3)  becomes

4×∠Q+∠Q=180  

=>5×∠Q=180  

=>∠Q=36  —————-(5)

From equations  (4)  and  (1) , we have

∠P=4×∠Q=4×36=144=∠R