Question

In the given parallelogram ABCD, find the value of x andy.

Answer 1

~Answer:

→ ∠y=37°

→ ∠x=36°

$\rule{380}{2}$

~Explanation:-

~Given:-

→ ∠A=3y°

→ ∠B=(2y-5)°

→ ∠C=(3x+3)°

$\rule{380}{2}$

~To find:-

→ Value of x and y

$\rule{380}{2}$

~Solution:-

Here in this question properties of parellelogram is used.

We know that parellelogram gram has following characteristics:

→ Opposite sides are equal.

→ Opposite angles are equal.

→ Sum of adjacent angles is 180°.

→ Opposite sides are parellel.

$\rule{380}{2}$

In the given figure, we can see that ∠A and ∠B are adjacent angles. So their sum will be 180°.

→ ∠A+ ∠B=180° [ Adjacent angles of ||gm]

Now put values of ∠A and ∠B.

→ 3y°+(2y-5)°=180°

→ 3y°+2y°-5°=180°

→ 5y°-5=180°

→ 5y°=180°+5°

→ 5y°=185°

Here both LHS and RHS have 5 as a common factor.

So let's divide 5 from both sides.

→ 5y÷5=185°÷5

→ y=37°

So the value of y is 37°.

$\rule{380}{2}$

Now we can see in the given figure that ∠A and ∠C are opposite angles of parellelogram. So these both angles will be equal.

→ ∠A=∠C   [Opposite angles of ||gm]

Put the given values of A and C.

→ 3y°=(3x+3)°

We have y=37°.

→ 3(37°)=3x+3°

→ 111°=3x+3°

→ 111°-3°=3x

→ 108°=3x

Divide 3 from both LHS and RHS.

→ 108°÷3=3x÷3

→ 36°=x

So the value of x is 36°.

$\rule{380}{2}$

Answer 2

Answer:

Step-by-step explanation:

By the property of parallelogram for angles

It is proven that internal angles of a parallelogram of same side bisecting transversal(BC) are supplementary.

So, (3x+3) + (2y-5) = 180

3x+2y = 182

Similarly, 3y+2y-5=180

y = 37

put the value of y in above equation

3x+2(37)=182

x = 36