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In the given figure, AOB is a diameter o...

In the given figure, AOB is a diameter of a circle and CD||AB. If `angle BAD = 30^(@)`, then `angle CAD` = ?

A

`30^(@)`

B

`60^(@)`

C

`45^(@)`

D

`50^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given that `CD||AB` and `angleBAD=30^(@)`
`becauseAOB` is the diameter.
`:. angleADB=90^(@) " (Angle in semicircle)"`
Now, In `DeltaADB,angleDAB+angleADB+angleABD=180^(@)`
`30^(@)+90^(@)+angleABD=180^(@)rArr angleABD=60^(@)`
`angleABD+angleACD=180^(@)`
`rArr60^(@)+angleACD=180^(@)rArr angleACD=120^(@)`
Also, `angleCDA=30^(@)=angleDAB" (Alternate angles)"`
In `DeltaCAD,angleCAD+angleCDA+angleACD=180^(@)`
`rArr angleCAD+30^(@)+120^(@)=180^(@)rArr angleCAD=30^(@)`
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