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 = 104o

ACE = 136o

ABD + ABC = 180o (Linear pair)

104o + ABC = 180o

ABC = 180o – 104o

= 76o

ACE + ACB = 180o

136o + ACB = 180o

ACB = 180o – 136o

= 44o


A + ABC + ACB = 180o

A + 76o + 44o = 180o

A + 120o = 180o

A = 180o – 120o

= 60o

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

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