Ex.5.1 Q4 Lines and Angles - NCERT Maths Class 7

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Question

 Find the angle which is equal to its complement.

Text Solution

 

What is known?

An angle which is equal to its complement.

What is the unknown?

Find measure of the angle.

Reasoning:

Let us say given angle is \(x\) and according to the question, its complement angle will also be equal to \(x\). The sum of angle and its complement angle is always equal to \(90^\circ.\)

Steps:

Solve for angle which is equal to its complement.

Let the angle be \(x\).

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

We know that, the sum of measure of pair of complementary angles is \(90^\circ.\)

\(x\) + \(x\) = \(90^\circ.\)

\(=>\) 2\(x\) = \(90^\circ.\)

\(=>\) \(x = \frac{90^\circ} {2}. \)

\(=>\) \(x\) = \(45^\circ.\)

Thus, the angle which is equal to its complement is \(45^\circ.\)