Question

Two adjective angles of a parallelogram have equal measure.Find the measures of each of the angels of the parallelogram.​

Answer 1

Let ABCD be the parallelogram with ∠A=∠B.

We know, sum of adjacent angles of parallelogram is 180

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⇒ ∠A+∠B=180

⇒ 2∠A=180

[ Since, ∠A=∠B ]

⇒ ∠A=90

⇒ ∠B=∠A=90

⇒ ∠A=∠C=90

[ Opposite angles of parallelogram ]

⇒ ∠B=∠D=90

[ Opposite angles of parallelogram ]

∴ Each angle of the parallelogram measures is 90

Answer 2

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Solution:-

It is given that,ABCD is a parallelogram in which two adjacent angales < A and < B have equal measure,say x.

m <A = x° and m < B = x°

As sum of any two adjacent angles of a parallelogram is 180°

➞ <A +<B = 180°

➞ x+x =180°

➞ 2x = 180°

➞ x = 90°

➞ <A+<B = 90°

Also, opposite of a parallelogram are equal.

< C = < A

< C = 90°

< D = <B

< D = 90°

hope it help uh!! ✌