Question

If $\mathit{x}$andwidth="59" height="20" role="math">2x-15 represent the measures of the acute angles of a right triangle, find the value of $\mathit{x}$.

Short answer

The value of$x$ is $\mathbf{35}$.

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,

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

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 $35$.