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

Question

The exterior angles, obtained on producing the base of a triangle both ways are 104&#xB0; and 136&#xB0;. Find all the angles of the triangle.

Philoid · Accepted Answer

Let, ABC be a triangle and base BC produced to both sides. Exterior angles are ∠ABD and ∠ACE.

∠ABD = 104^o

∠ACE = 136^o

∠ABD + ∠ABC = 180^o (Linear pair)

104^o + ∠ABC = 180^o

∠ABC = 180^o – 104^o

= 76^o

∠ACE + ∠ACB = 180^o

136^o + ∠ACB = 180^o

∠ACB = 180^o – 136^o

= 44^o

In

∠A + ∠ABC + ∠ACB = 180^o

∠A + 76^o + 44^o = 180^o

∠A + 120^o = 180^o

∠A = 180^o – 120^o

= 60^o

Thus, angles of triangle are 60^o, 76^o and 44^o.