Question

The measure of one of the small angles of a right triangle is $45$less than twice the measure of the other small angle. Find the measure of both angles.

Short answer

The measure of the angles are $45$ and $45$.

Step-by-step solution

Given information is,

The measure of one of the
small angles of a right triangle is
$45$ less than twice the measure of
the other small angle.

To find:

We need to find the measure of the two angles.

Let us consider,

$x$represents the measure of the first angle.

$y$represents the measure of the second angle.

We know that, for a right angle triangle,$x+y+90=180$.

It may also written as,

$$\begin{gathered} x+y=180-90 \\ x+y=90 \end{gathered}$$

It is given that,

The measure of one of the
small angles of a right triangle is
$45$ less than twice the measure of
the other small angle.

So,$x=2y-45$.

Step 5From the steps 3 and 4,

The obtained linear equations are,

$$\begin{gathered} x+y=90 \\ x=2y-45 \end{gathered}$$

Now we are going to find the required values by using the substitute method.

Substitute$x=2y-45$in the equation $x+y=90$.

$$\begin{gathered} 2y-45+y=90 \\ 3y+45=90 \\ 3y=90+45 \\ 3y=135 \\ y=\frac{135}{3} \\ y=45 \end{gathered}$$

Find the value of x.

Substitute the value of $y$in the equation $x+y=90$.

$$\begin{gathered} x+45=90 \\ x=90-45 \\ x=45 \end{gathered}$$