Question

The measures of the angles of a triangle are in the ratio of $2:3:5$. The measures of the angles are .

• A. ${36}^o,{54}^o,{90}^o$
• B. ${40}^o,{50}^o,{90}^o$
• C. ${30}^o,{50}^o,{110}^o$

Answer 1

The correct option is A ${36}^o,{54}^o,{90}^o$

$\underset{–}{ConceptInvolved:}$

Sum of interior angles of a triangle $={180}^o$

$\underset{–}{Method:}$

Let the angles of a triangle be $2x,3x$ and $5x$.
Since these are angles of a triangle, their sum would be ${180}^o$.

$\Rightarrow 2x+3x+5x={180}^o$
$\Rightarrow 10x={180}^o$

On dividing both sides of the equation by '$10$', we get,

$\Rightarrow \frac{10x}{10}=\frac{{180}^0}{10}$

$\Rightarrow x={18}^0$

$\because$ Angles are $2x,3x$ and $5x$.

$\therefore$ 1st angle $=2\times x=2\times {18}^o={36}^o$


Similarly, 2nd angle $=3\times x=3\times {18}^o={54}^o$

and the 3rd angle $=5\times x=5\times {18}^o={90}^o$

These angles form a right-angled triangle. Its angles are ${36}^0,{54}^0$ and ${90}^0$.