Question

The first of a triangle is one-third its second angle, whereas the third angle is $5$ times the first angle. Find the measure of all the angles of the triangle.

• A. $\angle a={100}^0$, $\angle b={20}^0$, $\angle c={60}^0$
• B. $\angle a={60}^0$, $\angle b={20}^0$, $\angle c={100}^0$
• C. $\angle a={20}^0$, $\angle b={60}^0$, $\angle c={100}^0$
• D. $\angle a={100}^0$, $\angle b={60}^0$, $\angle c={20}^0$

Answer 1

The correct option is C $\angle a={20}^0$, $\angle b={60}^0$, $\angle c={100}^0$

$Letthesecondangle=xthenfirstangle=\left(\frac{x}{3}\right)andthirdangle=\left(\frac{5x}{3}\right)nowx+\left(\frac{x}{3}\right)+\left(\frac{5x}{3}\right)={180}^{\circ }3x={180}^{\circ }\therefore x={60}^{\circ }soanglesare{20}^{\circ },{60}^{\circ },{100}^{\circ }$