Question

The outer angles of the triangle are in the ratio $4:5:6$. Find the measures of the smallest angle.

• A. $106°$
• B. $96°$
• C. $144°$
• D. $120°$

Answer 1

The correct option is B

$96°$

Let the angles be $4x$, $5x$ and $6x$.

The sum of the outer angles of the triangle is $360°$.

$\therefore 4x+5x+6x=360°$

$\Rightarrow 15x=360°$

$\Rightarrow x=24°$

Hence the measure of the angles are:
$4\times 24=96°,5\times 24=120°,6\times 24=144°$.

Hence the smaller angle is ${96}^{\circ }$.