If angle with measure x and y form a complementary pair, then angles with which of the following measures will form a supplementary pair?
a) (x+47°) , (y+43°)
b) (x-23°) , (y+23°)
c) (x-47°) , (y-43°)
d) (x+23°) , (y-23°)
Answers
Given : angle with measure x and y form a complementary pair,
To Find : angles with which of the following measures will form a supplementary pair?
a) (x+47°) , (y+43°)
b) (x-23°) , (y+23°)
c) (x-47°) , (y-43°)
d) (x+23°) , (y-23°)
Solution:
complementary pair add upto 90°
=> x + y = 90°
supplementary pair adds up to 180°
a) (x+47°) , (y+43°)
=> x + 47° + y + 43°
= x + y + 90°
= 90° + 90°
= 180°
Hence supplementary pair
(x-23°) , (y+23°)
=> x - 23° + y + 23°
= x + y
= 90°
not supplementary but complementary
(x-47°) , (y-43°)
=> x - 47° + y - 43°
= x + y - 90°
= 90° - 90°
= 0°
Hence not supplementary
(x+-23°) , (y-23°)
=> x +- 23° + y - 23°
= x + y
= 90°
not supplementary but complementary
(x+47°) , (y+43°) is the correct answer
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