Question

If the exterior angles of a triangles are in the ratio $1:3:5,$ find the angles.

• A. ${40}^o$
• B. ${60}^o$
• C. ${120}^o$
• D. ${200}^o$

Answer 1

Answer: (A), (C), (D)

${200}^o$

Let the exterior angles of the triangle be $\angle a,\angle b$ and $\angle c.$
As the angles are in the ratio $1:3:5,\angle a:\angle b=1:3$
$\therefore \angle b=3\angle a$
Similarly, $\angle c=5\angle a$

Now, we apply the fact that the sum of all the exterior angles of a triangle is ${360}^o.$

$\Rightarrow \angle a+\angle b+\angle c={360}^o$
$\Rightarrow \angle a+3\angle a+5\angle a={360}^o$
$\Rightarrow (1+3+5)\angle a={360}^o$
$\Rightarrow 9\angle a={360}^o$
$\Rightarrow \angle a=\frac{{360}^o}{9}={40}^o$

$\therefore \angle b=3\angle a=3\times {40}^o={120}^o$
Also, $\angle c=5\angle a=5\times {40}^o={200}^o$

$\therefore$ The 3 angles are ${40}^o,{120}^o$ and ${200}^o.$