In a right triangle, there are 2 acute angles and 1 right angle.
Let x be the measure of the larger acute angle, using the triangle sum theorem (that states that the sum of the interior angles of a triangle is 180) we have that:
[tex]\begin{gathered} x+\frac{1}{4}x+90=180 \\ \frac{5}{4}x=180-90 \\ \frac{5}{4}x=90 \\ 5x=360 \\ x=\frac{360}{5} \\ x=72 \end{gathered}[/tex]
The larger acute angle measures 72°.
