Question

The ratio of consecutive angles of a parallelogram is 2:3 find the angle

Answer 1

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$<b><u>Answer</u></b>$

$<b>∠A = 72°</b>$

$<b>∠B = 108°</b>$

$<b>∠C = 72°</b>$

$<b>∠D = 108°</b>$

$<b><u>Step-by-step explanation</u></b>$

$<b>Given that,</b>$

Ratio = 2:3

$<b>Let x be the consecutive angles.</b>$

$<b>Then the angles will be,</b>$

2x and 3x.

$<b>We know that,</b>$

The sum of all the angles of a quadrilateral is 360°. And opp. angles of a parallelogram are always equal.

Then, 2(2x + 3x) = 360°

4x + 6x = 360°

10x = 360°

x = $\frac{360°}{10}$

x = 36.

$<b>By substituting the value of x,</b>$

∠A = 2x = 2(36) = 72°

∠B = 3x = 3(36) = 108°

∠C = 2x = 2(36) = 72°

∠D = 3x = 3(36) = 108°

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Answer 2

let the ratio be 2x, 3x
2x + 3x = 180
5x = 180
x = 36
2x = 36 * 2 = 72°
3x = 3* 36 = 108°