Ex.5.1 Q5 Lines and Angles Solution- NCERT Maths Class 7

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Question

Find the angle which is equal to its supplement.

Text Solution

What is known?

An angle which is equal to its supplement.

What is the unknown?

Find measure of the angle.

Reasoning:

Let us say given angle is \(x\)  and according to the question, its supplementary angle will also be equal to \(x\). The sum of angle and its supplement angle is always equal to \(180^\circ.\)

Steps:

Let the angle be \(x.\)

Therefore, supplement of this angle will also be \(x.\)

We know that, the sum of measure of pair of supplementary angles is \(180 \,^{\circ}\)

\[\begin{align} x+x &=180^\circ\\ \Rightarrow2x &=180^\circ\\ \Rightarrow x&=(180^\circ)/2\\ \Rightarrow x&=90^\circ\end{align}\]

Thus, the angle which is equal to its supplement is \(90^\circ.\)