Ex.3.3 Q5 Understanding Quadrilaterals Solution-Ncert Maths Class 8

The measures of two adjacent angles of a parallelogram are in the ratio \({\rm{3}}:{\rm{2}}\). Find the measure of each of the angles of the parallelogram.

Text Solution

 What is Known?

Given figure is a parallelogram and two adjacent angles are having ratio of \({\rm{3}}:{\rm{2}}\) quadrilateral.

What is Unknown?

Measure of Each angles of parallelogram.

Reasoning:

A parallelogram is a quadrilateral whose opposite angles are equal.

Steps:

We know that the sum of the measures of adjacent angles is \(180º \) for a parallelogram.

\[\begin{align}\angle A + \angle B &= {180^{\rm{o}}}\\3x + 2x &= {180^{\rm{o}}}\\5x &= {180^{\rm{o}}}\\x &= \frac{{{{180}^{\rm{o}}}}}{5}\\x &= \,{36^{\rm{o}}}\end{align}\]

\[\begin{align} \angle A&=\angle C=3x \\ & ={{108}^{\circ}}\text{ }(\text{ Opposite angles }) \\  \angle B&=\angle D=2x \\ & ={{72}^{\circ}}\text{ (Opposite angles) }  \end{align}\]

Thus, the measures of the angles of the parallelogram are \(108^\circ, 72^\circ, 108^\circ,\) and \(72^\circ\).