Question

In the figure PQRS is a parallelogram.find the value of x and y

Answer 1

$\huge\underline\mathfrak\blue{Answer:}$

The value of x is 20 and y = 30.

Step-by-step explanation:

Property of parallelogram : Opposite angles of parallelogram are equal .

So, ∠P=∠R

Since we are given that ∠P=110°

∠R = (5x+10)°

So,  ∠P=∠R

110° =  (5x+10)°

110-10 =5x

100 = 5x

20 =x

So, ∠R = (5x+10)° = (5(20)+10)° = 110°

Property : Consecutive angles are supplementary i.e. sum of consecutive angles are 180°

⇒∠R+∠Q = 180°

⇒110°+(2y+10)° = 180°

⇒(2y+10)° = 180°-110°

⇒(2y+10) = 70

⇒2y = 70-10

⇒2y = 60

⇒y=30

Hence the value of x is 20 and y = 30.

Answer 2

Answer:

The value of x is 20 and y = 30.

Step-by-step explanation:

Property of parallelogram : Opposite angles of parallelogram are equal .

So, ∠P=∠R

Since we are given that ∠P=110°

∠R = (5x+10)°

So, ∠P=∠R

110° = (5x+10)°

110-10 =5x

100 = 5x

20 =x

So, ∠R = (5x+10)° = (5(20)+10)° = 110°

Property : Consecutive angles are supplementary i.e. sum of consecutive angles are 180°

⇒∠R+∠Q = 180°

⇒110°+(2y+10)° = 180°

⇒(2y+10)° = 180°-110°

⇒(2y+10) = 70

⇒2y = 70-10

⇒2y = 60

⇒y=30

Hence the value of x is 20 and y = 30.