Question

The measure of one of the small angles of a right triangle is $15$less than twice the measure of the other small angle. Find the measure of both the angles.

Short answer

The measure of the angles are $55$ and $35$.

Step-by-step solution

Step 1Given information is,

The measure of one of the
small angles of a right triangle is
$15$less than twice the measure of
the other small angle.

Step 2 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,$x+y+90=180$

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
$15$ less than twice the measure of
the other small angle.

So,$x=2y-15$

Step 5 From the steps 3and 4

The obtained linear equations are,

$$\begin{gathered} x+y=90 \\ x=2y-15 \end{gathered}$$

Now we are going to find the values of$x$and $y$by using the substitution method.

So, substitute $x=2y-15$in the equation $x+y=90$.

We get,

$$\begin{gathered} 2y-15+y=90 \\ -15+3y=90 \\ 3y=105 \\ y=\frac{105}{3} \\ y=35 \end{gathered}$$

Now find the value for x.

Substitute the value of $y=35$in the equation $x+y=90$.

$$\begin{gathered} x+35=90 \\ x=90-35 \\ x=55 \end{gathered}$$

Let us check the answer.

Substitute $x=55,y=35$into the equation $$\begin{gathered} x+y=90 \\ 55+35=90 \\ 90=90 \end{gathered}$$

which is true.