Q. 14.0( 19 Votes )

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

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}.

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