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Angles A and B are complementary and the...

Angles A and B are complementary and the measure of angle A is twice the measure of angle B. Find the measures of angles A and B

A

`angleA=20^(@),angleB=40^(@)`

B

`angleA=30^(@),angleB=60^(@)`

C

`angleA=60^(@),angleB=30^(@)`

D

`angleA=15^(@),angleB=30^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Here `angleA+angleB=90^(@) " ".....(1)` (given as these are complementary angles)
Also, `angleA=2angleB" ".....(2)` (given)
Putting the value of `angle A ` form (2) in (1), we get
`2angleB+angleB=90^(@)`
`rArr 3angleB=90^(@)`
`rArr angleB=30^(@)`
`:.angleA=2xx30^(@) " "` [ from (2)]
`=60^(@)`
Hence, `angleA=60^(@),angleB=30^(@)`
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