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7. An angle is 36° more than its complement. Find the angles.
Two complementary angles are in the ratio 2:3, find their measure.
Two supplementary angles are (2x - 5) and (7x + 5)º, find the angles.
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Answers
Answer with Step-by-step explanation:
a... Let the complement be x and the angle be x + 36°
We know, sum of complementary angles is 90°
x + 36 + x = 90
2x + 36 = 90
x = 90 - 36/2
x = 27°
Hence, the complement angle = x = 27° and,
the angle = x + 36 = 27 + 36 = 63°
b... Let the angles be 2x and 3x
We know, sum of complementary angles is 90°
So, 2x + 3x = 90
5x = 90
x = 90/5
x = 18°
Hence, one angle = 2x = 2 X 18
= 36°
and the other angle = 3x = 3 X 18
= 54°
c...Two supplementary angles are (2x - 5)º and (7x + 5)º
We know, sum of supplementary angles is 180º
So, (2x - 5)º + (7x + 5)º = 180º
2x - 5 + 7x + 5 = 180 ( as -5 and 5 cancels each other )
9x = 180
x = 180/9
x = 20º
Hence, one of the angle = (2x - 5)º = 2 X 20 - 5
= 35º
and, the other = (7x + 5)º = 7 X 20 + 5
145º
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