On a semi-circle with A B as diamete...

On a semi-circle with `A B` as diameter, a point `C` is taken, so that `m\ (/_C A B)=30^@dot` Find `m\ (/_A C B)a n d\ m(/_A B C)`

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Solution
A semicircle with `AB` as diameter
`/_CAB=30^@/_ACB=90^@` (Angle in a semi circle)But
`/_CAB+/_ACB+/_ABC=180^@`
`=>30^@+90^@+/_ABC=180^@`
`=>120^@+/_ABC=180^@`
`∴/_ABC=180^@−120^@=60^@`
Hence,
`/_ACB=90^@and /_ABC=60^@`

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