Question

Find the unknown marked angles in the given figure:

Answer 1

We know that in a triangle if one side of it is produced, then

Exterior angle = sum of its interior opposite angles.

In fig., 125° = a + c .......(i)
and 140° = a + b ............(ii)

Adding, we get

a + c + a + b = 125° + 140°

⇒ a + a + b + c = 265°
But a + b + c = 180° ........(sum of angles of a triangle)

∴ a + 180° = 265°

⇒ a = 265° − 180° = 85°
But a + b = 140°

⇒ 85° + b = 140°

⇒ b = 140°− 85° = 55°

and a + c = 125°

⇒ 85° + c = 125°

⇒ c = 125° − 85° = 40°

Hence a = 85°, b = 55° and c = 40°