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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