Question

The ratio of two acute angles of a right triangle is $4:5$. The smaller acute angle is$\_\_\_\_\_\_\_$

Answer 1

Given

The triangle is right-angled so one of its angles is $90°$

Let the two angles of a triangle be $4xand5x$

$\because$ The sum of all angles in a triangle is $180°$

$$\begin{gathered} \Rightarrow 4x+5x+90=180 \\ \Rightarrow 9x+90=180 \\ \Rightarrow 9x=180-90 \\ \Rightarrow 9x=90 \\ \Rightarrow x=\frac{90}{9} \\ \Rightarrow x=10° \end{gathered}$$

so, three angles of the triangle are $90°$

$$\begin{gathered} 4x=4\times 10=40°and \\ 5x=5\times 10=50° \end{gathered}$$

Hence, the measure of the smaller acute angle is $40°$.