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 angles.

Short answer

The measures of the angles are$55$and$35$

Step-by-step solution

Step 1. Given information

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. Find the angles

Let angles to be $x$and $y$

$x+y=90$

Now using the given condition,

$x=2y-15$

Put this value of $x$in other equation,

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

Now put this value of $y$in any of the equation,

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

The measures of the angles are $35$ and$55$

Step 3. Check by substituting values in both the equations

Substitute $x=55,y=35$in both the equations

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

This is true

$$\begin{gathered} x=2y-15 \\ 55=2\left(35\right)-15 \\ 55=70-15 \\ 55=55 \end{gathered}$$

This is also true