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

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Let, ABC be a triangle and base BC produced to both sides.

Exterior angles are ∠ABD and ∠ACE.

∠ABD = 104°

∠ACE = 136°

∠ABD + ∠ABC = 180°(Linear pair)

104° + ∠ABC = 180°

∠ABC = 180° – 104°

= 76°

∠ACE + ∠ACB = 180°

136° + ∠ACB = 180°

∠ACB = 180° – 136°

= 44°

In ΔABC

∠A + ∠ABC + ∠ACB = 180°

∠A + 76° + 44° = 180°

∠A + 120° = 180°

∠A = 180° – 120°

= 60°

Thus, angles of triangle are 60° , 76° and 44°.

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