Question

In a right triangle one of the acute angles is 1/4 the size of the other acute angle find the measure of the larger angle

Answer 1

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:

`\begin{gathered} x+(1)/(4)x+90=180 \\ (5)/(4)x=180-90 \\ (5)/(4)x=90 \\ 5x=360 \\ x=(360)/(5) \\ x=72 \end{gathered}`

The larger acute angle measures 72°.