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In the given figure, the lines AB, CD an...

In the given figure, the lines AB, CD and EF intersect at a point O. If `angleBOD= x^(@), angleAOE= 2x^(@) and angleCOF= 90^(@)`, find `angleAOE and angleAOC`

A

`30^@`

B

`40^@`

C

`55^@`

D

`70^@`

Text Solution

Verified by Experts

The correct Answer is:
A
`/_EOD = /_FOC` (Vertically Opposite Angles)
So,` /_ EOD = 90^@`
`/_ EOA + /_ EOD + /_ DOB = 180^@` (supplementary angles)
So, `2x + x + 90^@ = 180^@`
`3x = 90^@`
`x = 30^@`
Therefore, angle `x` is equal to `30^@`.
`/_ AOE = 2 xx 30^@ = 60^@`
`/_AOC = 180^@ - (90^@ + 60^@)` [Supplementary Angles]
`= 180^@ - 150^@`
`= 30^@`
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