On a semi-circle with AB as diameter, a point C is taken, so that m ( ∠ CAB )= 30°. Find m ( ∠ ACB ) and m ( ∠ ABC ).

Question

On a semi-circle with AB as diameter, a point C is taken, so that m ( &#x2220; CAB )= 30&#xB0;. Find m ( &#x2220; ACB ) and m ( &#x2220; ABC ).

Philoid · Accepted Answer

We have,

∠CAB = 30^o

∠ACB = 90^o (Angle in semi-circle)

IN triangle ABC, by angle sum property

∠CAB + ∠ACB + ∠ABC = 180^o

30^o + 90^o + ∠ABC = 180^o

∠ABC = 60^o