Question

If x and$2x-15$ represent the measures of the acute angles of a right triangle, find the value of x.

Short answer

The value of x is 35.

Step-by-step solution

Step 1. Apply the definition of right-angled triangle.

A right-angled triangle is a type of triangle in which measure of one of its angles is 90 degrees.

Step 2. Apply an angle sum theorem.

The sum measure of all angles of a triangle is 180°.

According to given condition,

$\begin{array}{c}x+2x-15+90=180\\ 3x-15+90=180\\ 3x=180-75\\ =105\end{array}$

Step 3. Description of step.

Divide each side of the obtained equation in step 2 by 3 to find the value of x.

$\begin{array}{c}\frac{3x}{3}=\frac{105}{3}\\ x=35\end{array}$

Therefore, the value of x is 35.