# Ex.5.1 Q8 Lines and Angles - NCERT Maths Class 7

## Question

An angle is greater than \(45^\circ.\) Is its complementary angle greater than \(45^\circ\) or equal to \(45^\circ\) or less than \(45^\circ\,?\)

## Text Solution

**Reasoning:**

Let us represent the angle by \(\angle 1\) and its complement angle by\( \angle 2.\) Let’s visually model this problem. There are two operations done in sequence. First take\( \angle 1\,\, \gt 45^\circ\) as it is given, and then add \(\angle 2\) to both sides of the equation.

According to this model, the result is equal to \(\angle 1 + \angle 2\,\, \gt 45 ^\circ + \angle 2.\) Now, it’s a matter of finding Is its complementary angle greater than \(45^\circ\) or equal to \(45^\circ\) or less than \(45^\circ.\)

**Steps:**

Let there be two angles \(\angle 1\) and \(\angle 2 .\)

Therefore\( \angle 1 \gt 45^\circ\) (given)

Adding \(\angle 2\) to both sides ,we get

\(=\gt \angle 1 + \angle 2 \gt 45^\circ + \angle 2\\ =\gt 90^\circ \gt 45^\circ + \angle 2 \\ =\gt 90^\circ - 45^\circ \gt \angle 2 \\ =\gt 45^\circ \gt \angle 2\)

Therefore, its complementary angle will be less than \(45^\circ.\)