Question

One side of a triangle is extended in both directions. If the two exterior angles thus produced be 106°and125° then find the angles of the triangle.

Answer 1

Answer:

Draw a triangle ABC and extend BC such that exterior <B = 125° and exterior <C = 106°

<ABD + <ABC = 180° ...... (LINEAR PAIR)

Since, <ABD = 125°

125° + <ABD = 180°

<ABD = 55°

<ACE + <ACB = 180° ......... (LINEAR PAIR)

Since,<ACE = 106°

106° + <ACB = 180°

<ACB = 74°

In triangle ABC,

<A + <B + <C = 180°

<B = 55°

<C = 74°

<A + 55° + 74 °= 180°

<A + 129° = 180°

<A = 51°

All angles of triangle are - 74° , 55° , 51°