Question

2) ABCD is quadrilateral and their ratio is 2: 3:4:1. Find measures of all angles and
write type of quadrilateral.
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Answer 1

✲Question:-

• ABCD is quadrilateral and their ratio is 2: 3:4:1. Find measures of all angles and write type of quadrilateral.

Given:-

• The ratio of angles are 2:3:4:1

To find:-

• Measure of all angles

Solution:-

• Let the angles of a quadrilateral be 2x,3x,4x,1x

We know that the sum of angles of a quadrilateral = 360°

$\implies \: 2x + 3x + 4x + 1x = 360 \degree$

$\implies \: 10x = 360 \degree$

$\implies \: x = \frac{360}{10}$

$\implies \: x = 36$

Therefore the measures of angles:-

• 2x= 2×36=72°
• 3x=3×36=108°
• 4x=4×36=144°
• 1x=1×36=36°

Suppose

∠A=72° and ∠B=108°

$\sf \: Sum \: \: of \:  ∠A \:  and  \: ∠B=72 \degree \: +108 \degree \: =180 \degree$

This means, AB is a transversal to the parallel sides AD and BC as the sum of

interior angles on the same side of transversal is 180°

Hence, AD||BC and ABCD is a trapezium.

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