Identify which of the following pairs of angles are complementary and which are supplementary:
(i) 65o, 115o
(ii) 63o, 27o
(iii) 112o, 68o
(iv) 130o, 50o
(v) 45o, 45o
(vi) 80o, 10o
(i) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 115o and 65o
Therefore,
Sum of the measures of these angles = 115o + 65o
= 180o
As the sum of these angles is equal to 180o
Therefore,
These angles are supplementary angles.
(ii) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 63o and 27o
Therefore,
Sum of the measures of these angles = 63o + 27o
= 90o
As the sum of these angles is equal to 90o
Therefore,
These angles are complementary angles
(iii) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 112o and 68o
Therefore,
Sum of the measures of these angles = 112o + 68o
= 180o
As the sum of these angles is equal to 180o
Therefore,
These angles are supplementary angles
(iv) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 130o and 50o
Therefore,
Sum of the measures of these angles = 130o + 50o
= 180o
As the sum of these angles is equal to 180o
Therefore,
These angles are supplementary angles
(v) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 45o and 45o
Therefore,
Sum of the measures of these angles = 45o + 45o
= 90o
As the sum of these angles is equal to 90o
Therefore,
These angles are complementary angles
(vi) We know that,
Sum of measures of supplementary angles is 180o
Also,
Sum of measures of complementary angles is 90o
It is given in the question that,
The two pairs of angles are 80o and 10o
Therefore,
Sum of the measures of these angles = 80o + 10o
= 90o
As the sum of these angles is equal to 90o
Therefore,
These angles are complementary angles