In the figure, ABC is a triangle in which AB = AC. Find x° and y°.

Theorem 2:

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

∠ ACE + ∠ ACB = 180°

⇒ x + 48° + x° = 180°

⇒ 2x + 48° = 180°

⇒ 2x = 180° - 48°

⇒ 2x = 132°

⇒

⇒ x = 66°

Ext. ∠ A = ∠ B + ∠ C

⇒ y° = x° + x°

⇒ y° = 2x°

⇒ y° = 2 × 66°

⇒ y° = 132°