Question

The exterior angles, obtained on producing the base .of a triangle both ways, are ${102}^{\circ }$ and ${134}^{\circ }$. Find the smallest angle of the triangle.

• A. ${56}^o$
• B. ${78}^o$
• C. ${46}^o$
• D. none of the above

Answer 1

The correct option is C ${46}^o$

Let the triangle be ABC, with ${102}^{\circ }$ formed by extending along B and ${134}^{\circ }$ be formed by extending along C
Thus, $\angle A+\angle C=102$ (Exterior angle is equal to sum of interior opposite angles)
$\angle A+\angle B=134$ (Exterior angle is equal to sum of interior opposite angles)
Adding the two equations,
$\angle A+\angle A+\angle B+\angle C=236$
we know, $\angle A+\angle B+\angle C=180$ (Sum of angles of a triangle)
Hence, $\angle A=236-180$
$\angle A=56$
Thus, $\angle B=134-56=78$
$\angle C=102-56=46$