Question

$\begin{gathered}\begin{gathered}\sf \large \red{\underline{ Question:-}}\\\\\end{gathered}\end{gathered}$

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

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Answer 1

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180⁰

⇒3x+2x=180⁰

⇒5x=180⁰

⇒x= $\dfrac{180}{5}$ =36⁰

∴∠3×36⁰

=108⁰

and, ∠B=2×36⁰

=72⁰

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108⁰and ∠D=∠B=72⁰

Hence, ∠A=108⁰,∠B=72⁰,∠C=108 ⁰and ∠D=72⁰

Answer 2

Answer:

explanation

Explanation:

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180⁰

⇒3x+2x=180⁰

⇒5x=180⁰

⇒x= \dfrac{180}{5}

5

180

=36⁰

∴∠3×36⁰

=108⁰

and, ∠B=2×36⁰

=72⁰

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108⁰and ∠D=∠B=72⁰

Hence, ∠A=108⁰,∠B=72⁰,∠C=108 ⁰and ∠D=72⁰