Theorem

Sum of the angles of a triangle is equal to two right angles.

ABC is a triangle

A + B + ACB = 180^o

Produce BC to D. Through C draw CE || BA.

Corollary of Theorem

If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles.

In ABC, BC is produced to D.

If in a triangle ABC, the bisectors of the angles ABC and ACB meet at M, prove that

(Sum of angles of a D = 180^o)

Also ( MB bisects )

( MC bisects )

…(1)

In

(Sum of the angles of a = 180^o)

Using (1)

BMC = 180^O - (CBM + BCM)

or (Proved)