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In DeltaABC it is given that angleA=70^(...

In `DeltaABC` it is given that `angleA=70^(@),angleB=52^(@),BOandCO` are the bisectors of `angleBandangleC` respectively. Find `angleOCBandangleBOC`.

A

29 and 125

B

26 and 125

C

56 and 125

D

58 and 56

Text Solution

Verified by Experts

The correct Answer is:
A
We know that the sum of the angles of a triangle is `180^(@)`.
`:.angleA+angleB+angleC=180^(@)`
`implies70^(@)+52^(@)+angleC=180^(@)`
`impliesangleC=(180^(@)-122^(@))=58^(@)=29^(@)`
and `angleOBC=(1)/(2)angleC=((1)/(2)xx58^(@))=26^(@)`. In `DeltaBOC`, we have
`angleOBC+angleOCB+angleBOC=180^(@)`
`26^(@)+29^(@)+angleBOC=180^(@)`
`impliesangleBOC=(180^(@)-55^(@))=125^(@)`.
Hence, `angleOCB=29^(@)andangleBOC=125^(@)`.
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