Math, asked by prajwalamagaji123, 6 months ago

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

Answers

Answered by bhavyanshisinghalvi2
2

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Answered by sᴜɢᴀʀsᴜᴘ
9

 \huge \underline\red{Question}

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

 \huge\underline\red{Solution}

Let two adjacent angles be A and B of measures 3x and 2x respectively.

Now,

3x + 2x = 180°

(adjacent angles are supplementary)

5x = 180°

x =  \frac{180}{5}

 = 36°

∠A = 3x = 3 \times 36 = 108°

∠</strong><strong>A</strong><strong> = 108°

∠</strong><strong>B</strong><strong> = 2x = 2 \times 36 = 72°

∠</strong><strong>B</strong><strong> = 72°

∠</strong><strong>C</strong><strong> = ∠</strong><strong>A</strong><strong> = 108°

(Opposite angles are equal)

∠</strong><strong>C</strong><strong> = 108°

∠</strong><strong>D</strong><strong> = ∠</strong><strong>B</strong><strong> = 72°

(Opposite sides are equal)

∠</strong><strong>D</strong><strong> = 72°

Hence all angles of ||gm are ∠A=72°, ∠B=108°, ∠C =72°, ∠D =108°.

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