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

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Question

Find \(x\) in the following figures.

 Video Solution
Understanding Quadrilaterals
Ex 3.2 | Question 1

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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