Question

The acute angles of the right-angled triangle are in the ratio $4:5$, the measure of the angles are _____

• A. $50°,40°$
• B. $20°,70°$
• C. $40°,50°$
• D. $5°,85°$

Answer 1

The correct option is C

$40°,50°$

The acute angles of the right-angled triangle are in the ratio $4:5$

So, one angle will be $4x$ and other angle will be $5x$.

As it is a right-angled triangle, the remaining angle will be $90°$.

By angle sum propety,

$4x+5x+90°=180°$

$9x+90°=180°$

$9x=180°-90°$

$9x=90°$

$x=\frac{90°}{9}$

$x=10°$

So, one angle of the right-angled triangle is $4x$$=4\times 10°=40°$

the other angle is $5x$$=5\times 10°=50°$.

Therefore, the measure of the acute angles are $40°,50°$

Hence, option C is the correct option.