Question

The acute angles of a right-angled triangle are in the ratio $2:3$. The measures of these angles are………………….

• A. $28,62$
• B. $36,54$
• C. $40,50$
• D. $30,45$

Answer 1

The correct option is B

$36,54$

The sum of acute angles in a right-angled triangle is $90$.

Given that, the ratio of acute angles = $2:3$

Since, the sum of parts = $2+3=5$

So, the measure of first angle $=\frac{2}{5}\times 90=2\times 18=36°$

and the measure of second angle $=\frac{3}{5}\times 90=3\times 18=54°$

Hence, the measure of acute angles are $36,54$.