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Identify which of the following pairs of angles are complementary and which are supplementary.
$(i).\ 65^{\circ},\ 115^{\circ}$
$(ii).\ 63^{\circ},\ 27^{\circ}$
$(iii).\ 112^{\circ},\ 68^{\circ}$
$(iv).\ 130^{\circ},\ 50^{\circ}$
$(v).\ 45^{\circ},\ 45^{\circ}$
$(vi).\ 80^{\circ},\ 10^{\circ}$
To do:
We have to identify which of the given pairs of angles are complementary and which are supplementary.
Solution:
Complementary angles:
Two angles are said to be complementary if the sum of their measures is $90^o$.
Supplementary angles:
Two angles are said to be supplementary if the sum of their measures is $180^o$.
Therefore,
(i) $65^{\circ}+115^{\circ}=180^{\circ}$
They are supplementary angles.
(ii) $63^{\circ}+27^{\circ}=90^{\circ}$
They are complementary angles.
(iii) $112^{\circ}+68^{\circ}=180^{\circ}$
They are supplementary angles.
(iv) $130^{\circ}+50^{\circ}=180^{\circ}$
They are supplementary angles.
(v) $45^{\circ}+45^{\circ}=90^{\circ}$
They are complementary angles.
(vi) $80^{\circ}+10^{\circ}=90^{\circ}$
They are complementary angles.