Question

The exterior angles obtained on producing the base of a triangle both ways are 104° and 136°. Find the angles of the triangle.

Answer 1

Given: ∠ABD = 104° and ∠ACE = 136°

To find: ∠A, ∠B and ∠C

Solution:

We know that an exterior angle is equal to the sum of its interior opposite angles.

∠2 + ∠3 = ∠ABD

∠2 + ∠3 = 104° ... (1)

∠2 + ∠1 = ∠ACE

∠2 + ∠1 = 136° … (2)

Also, ∠1 + ∠2 + ∠3 = 180° (Sum of angles of triangle)

136° + ∠3 = 180° (Using (2))

∠3 = 180° − 136°

∴∠3 = 44°

We have ∠2 + ∠3 = 104°

∠2 + 44° = 104°

∠2 = 104° − 44°

∴∠2 = 60°

We have ∠2 + ∠1 = 136°

60° + ∠1 = 136°

∠1 = 136° − 60°

∴∠1 = 76°

Thus, the angles of the triangle are .