two complementary angles are in the ratio 1:2 , when 15 is added to the smaller angle and 15 is subtracted from the bigger angle, the ratio of the angles became 1:1 , find the angles.
Answers
Answer:
30 and 60
Step-by-step explanation:
2 complementary angles are given
That is : x and 90-x
Given that
x/90-x = 1/2
2x = 90 - x
3x = 90
x = 90/3
x = 30
90-x = 60
30+15 = 45
60-15 = 45
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SOLUTION
GIVEN
- Two complementary angles are in the ratio 1 : 2
- When 15 is added to the smaller angle and 15 is subtracted from the bigger angle , the ratio of the angles became 1 : 1
TO DETERMINE
The angles
EVALUATION
Here it is given that the angles are in the ratio 1 : 2
Let smaller angle = x and bigger angle = 2x
Since the angles are complementary angles
x + 2x = 90°
⇒ 3x = 90°
⇒ x = 30°
Smaller angle = 30°
Bigger angle = 2 × 30° = 60°
Verification :
When 15 is added to the smaller angle
Then angle becomes
= 30° + 15°
= 45°
When 15 is subtracted from the bigger angle
Then angle becomes
= 60° - 15°
= 45°
The ratio becomes
= 45° : 45°
= 1 : 1
FINAL ANSWER
Smaller angle = 30°
Bigger angle = 60°
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