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Question
On a semi-circle with AB as diameter, a point C is taken, so that m (∠CAB) = 30°. Find m(∠ACB) and m (∠ABC).
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Solution
It is given that, AB as diameter, O is centre and`angle CAB = 30°`
We have to find `m angleACB` and ` m angleABC`
Since angle in a semi-circle is a right angle therefore
`angleACB = 90°`
In Δ ACD we have
`angleCAB` = 30° (Given)
`angleACB `= 90° (Angle in semi-circle is right angle)
Now in Δ ACB we have
`angleCAB + angleACB + angleABC `= 180
`angleABC = 180° - (angle CAB + angleCAB )`
=180° - (90° + 30° )
= 180° - 120°
= 60°
Hence `angle ABC = 60°` and `angleACB = 90°`
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