If one angle of a triangle is equal to the sum of the two other angles, show that the triangle is right – angled.

The side BC of ΔABC has been increased on both sides as shown. If ∠ABD = 105° and ∠ACE = 110°, then find ∠A.

Prove that the bisectors of two adjacent supplementary angles include a right angle.

In the given figure, ACB is a straight line and CD is a line segment such that ∠ACD = (3x – 5)° and ∠BCD = (2x + 10)°. Then, x = ?

In the given figure, AOB is a straight line. If ∠AOC = 40°, ∠COD = 4x° and ∠BOD = 3xׄ°, then x = ?