17 A Rs Aggarwal Chapter 17 Class 7 ICSE
Let’s solve both problems step by step.
1. Find an angle which is two-thirds of its complement.
Let the angle be x.
Its complement is (90 - x) (since complementary angles add up to 90°).
According to the question:
x = (2/3)(90 - x)
Now solve for x:
x = (2/3)(90 - x)
Multiply both sides by 3 to eliminate the fraction:
3x = 2(90 - x)
3x = 180 - 2x
Add 2x to both sides:
5x = 180
x = 36
Answer: The angle is 36°.
2. Find an angle which is one-fifth of its supplement.
Let the angle be y.
Its supplement is (180 - y) (since supplementary angles add up to 180°).
According to the question:
y = (1/5)(180 - y)
Now solve for y:
y = (1/5)(180 - y)
Multiply both sides by 5:
5y = 180 - y
Add y to both sides:
6y = 180
y = 30
Answer: The angle is 30°.
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