# Ex.5.1 Q3 Lines and Angles - NCERT Maths Class 7

## Question

Identify which of the following pairs of angles are complementary and which are supplementary:

(i) \(65^\circ, 115^\circ\)

(ii) \(63^\circ, 27^\circ\)

(iii) \(112^\circ, 68 ^\circ\)

(iv) \(130^\circ, 50^\circ\)

(v) \(45^\circ, 45^\circ\)

(vi) \( 80^\circ, 10^\circ\)

**NOTE: **The sum of the measure of complementary angle is \(90^\circ\) and that of supplementary angle is \(180^\circ\)

## Text Solution

**Reasoning:**

Find out the sum of two given angles,and then check whether it is \(180^\circ\) or \(90^\circ.\) If the sum of two angles is either equal to \(90^\circ\), the angles are complementary and if the sum of the two angles is \(180^\circ\), the angles are complementary.

**Steps:**

Solve for supplementary angle or complementary angle:

(i) \(65^\circ, 115^\circ\)

Sum of measure of these two angles \(= 65^\circ + 115^\circ = 180^\circ\)

Therefore, these two angles are supplementary.

(ii) \(63^\circ, 27^\circ\)

Sum of measure of these two angles \(= 63^\circ + 27^\circ = 90^\circ\)

Therefore, these two angles are complementary.

(iii) \(112^\circ, 68^\circ\)

Sum of measure of these two angles \(= 112^\circ + 68^\circ = 180^\circ\)

Therefore, these two angles are supplementary.

(iv) \(130^\circ, 50^\circ\)

Sum of measure of these two angles \(= 130^\circ + 50^\circ = 180^\circ\)

Therefore, these two angles are supplementary.

(v) \(45^\circ, 45^\circ\)

Sum of measure of these two angles \(= 45^\circ + 45^\circ = 90^\circ\)

Therefore, these two angles are complementary.

(vi) \(80^\circ, 10^\circ\)

Sum of measure of these two angles \(= 80^\circ + 10^\circ = 90^\circ\)

Therefore, these two angles are complementary.

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