Question

In a right angled triangle , the 2 smaller angles are in the ratio 1 : 5. Find the measure of the smallest angle

• A. ${20}^{\circ }$
• B. ${15}^{\circ }$
• C. ${12}^{\circ }$
• D. ${24}^{\circ }$

Answer 1

The correct option is B

${15}^{\circ }$

In a right angled triangle , the sum of 2 angles apart from the right angle = ${90}^{\circ }$

Let the smaller of these angles be x and the larger be 5x ( According to the ratio given)

x + 5x = ${90}^{\circ }$

$\Rightarrow$ 6x = ${90}^{\circ }$

$\Rightarrow$ x = $\frac{90}{6}$ = ${15}^{\circ }$

Hence the measure of the smallest angle= ${15}^{\circ }$