Question

The angles of a triangle are 30°, 40° and 110°. Find the measures of its external angles.

Answer 1

Given: ΔABC with ∠A = 30°, ∠B = 40° and ∠C = 110°

The measures of the external angles of a triangle can be calculated using the property of linear pair.

We know that the sum of the measures of angles forming a linear pair is 180°.

⇒ ∠ACS + ∠ACB = 180°

⇒ ∠ACS = 180° − 110°

= 70°

Similarly, ∠CBU + ∠CBA = 180°

⇒ ∠CBU + 40° = 180°

⇒ ∠CBU = 180°− 40°

= 140°

∠CAT + ∠CAB = 180°

⇒ ∠CAT = 180° − 30°

= 150°

Thus, the measures of the external angles of the given triangle are 150°, 140° and 70°.