Question

The ratio of three angles of a triangle is $1:9:5$. Find the smallest angle.

• A. ${12}^o$
• B. ${150}^o$
• C. ${90}^o$
• D. ${45}^o$

Answer 1

The correct option is A ${12}^o$

Let the three angles of triangle $x$, $9x$, $5x$

$x+9x+5x={180}^o$

$⟹15x={180}^o$

$⟹x=\frac{180}{15}$

$x={12}^o$

Therefore the three angles are $x={12}^0$, $9x=9\times 12={108}^0$, $5x=5\times 12={60}^0$

so the smallest angle is ${12}^o$