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

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## Question

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

Video Solution
Lines & Angles
Ex 5.1 | Question 8

## 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 $$45^\circ.$$

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