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

(i) 65^{o}, 115^{o}

(ii) 63^{o}, 27^{o}

(iii) 112^{o}, 68^{o}

(iv) 130^{o}, 50^{o}

(v) 45^{o}, 45^{o}

(vi) 80^{o}, 10^{o}

(i) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 115^{o} and 65^{o}

Therefore,

Sum of the measures of these angles = 115^{o} + 65^{o}

= 180^{o}

As the sum of these angles is equal to 180^{o}

Therefore,

These angles are supplementary angles.

(ii) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 63^{o} and 27^{o}

Therefore,

Sum of the measures of these angles = 63^{o} + 27^{o}

= 90^{o}

As the sum of these angles is equal to 90^{o}

Therefore,

These angles are complementary angles

(iii) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 112^{o} and 68^{o}

Therefore,

Sum of the measures of these angles = 112^{o} + 68^{o}

= 180^{o}

As the sum of these angles is equal to 180^{o}

Therefore,

These angles are supplementary angles

(iv) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 130^{o} and 50^{o}

Therefore,

Sum of the measures of these angles = 130^{o} + 50^{o}

= 180^{o}

As the sum of these angles is equal to 180^{o}

Therefore,

These angles are supplementary angles

(v) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 45^{o} and 45^{o}

Therefore,

Sum of the measures of these angles = 45^{o} + 45^{o}

= 90^{o}

As the sum of these angles is equal to 90^{o}

Therefore,

These angles are complementary angles

(vi) We know that,

Sum of measures of supplementary angles is 180^{o}

Also,

Sum of measures of complementary angles is 90^{o}

It is given in the question that,

The two pairs of angles are 80^{o} and 10^{o}

Therefore,

Sum of the measures of these angles = 80^{o} + 10^{o}

= 90^{o}

As the sum of these angles is equal to 90^{o}

Therefore,

These angles are complementary angles

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