Question

6. In Figure 21. ABCD is a parallelogram. Find the measures of x and y​

Answer 1

Given:-

ABCD is a parallelogram

To find:-

measures of x and y

Solution:-

using,

Theorem 1:- opposite angles are equal in a parallelogram.

Here, ∠A and ∠C are opposite angles

So, ∠A=∠C

$\longrightarrow3x + 15 = 2x + 35$

$\longrightarrow3x - 2x = 35 - 15$

$\longrightarrow \: x = 20$

using,

Theorem 2:- adjecent angles are supplementary(sum to 180°) in a parallelogram

Here, ∠A and ∠B are supplementary

So, ∠A+ ∠B=180°

$3x + 15 = 2y + 5$

$3(20) + 15 = 2y + 5$

$75 - 5 = 2y$

$2y = 70$

$y = \frac{70}{2}$

$y = 35$

Final answer:-

x=20

y=35

THANK YOU

Answer 2

Answer:

Step-by-step explanation:

Theorem 1:- opposite angles are equal in a parallelogram.

Here, ∠A and ∠C are opposite angles

So, ∠A=∠C

using,

Theorem 2:- adjecent angles are supplementary(sum to 180°) in a parallelogram

Here, ∠A and ∠B are supplementary

So, ∠A+ ∠B=180°

Final answer:-

x=20

y=35