# Ex.3.2 Q1 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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## Question

Q1. Find $$x$$ in the following figures.

## Text Solution

What is Known?

Other angles of given polygon.

What is Unknown?

Angle $$x$$ in the above figures $$a$$ and $$b$$.

Reasoning:

We know that the sum of the measures of the exterior angles of any polygon is $$360^\circ$$ So equate all the angle sum to $$360^\circ$$ and find out the unknown angle.

Steps:

(a)

Sum of the measures of the external angles,

\begin{align}125^\circ \, + 125^\circ \, + \,x\, = \,360^\circ \\{\rm{25}}0^\circ + {\rm{ }}x{\rm{ }} = {\rm{ 36}}0^\circ \\x{\rm{ }} = {\rm{ 11}}0^\circ\end{align}

(b)

\begin{align}y &= {{{180}^{\rm{\circ}}} - {{90}^{\rm{\circ}}}\quad {\text{[linear pair angles]}}}\\ y &= {{90}^{\rm{\circ}}}\end{align}

Sum of the measures of the external angles is $$360^\circ$$,

\begin{align}60^\circ + 90^\circ + 70^\circ + {\rm{ }}x{\rm{ }} + y &= {360^{\rm{\circ}}}\\ {\rm{6}}0^\circ + {\rm{9}}0^\circ + {\rm{7}}0^\circ + {\rm{ }}x{\rm{ }} + {\rm{ 9}}0^\circ &= {\rm{36}}0^\circ \\{\rm{31}}0^\circ + x &= {\rm{36}}0^\circ \\x &= {\rm{5}}0^\circ\end{align}

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