Question

The measure of one of the

small angles of a right triangle is

14 more than 3 times the measure

of the other small angle. Find the

measure of both angles.

Short answer

The measure of angles are$19$and$71$.

Step-by-step solution

Step 1. Given information

A right-angled triangle such that $x$and $y$represents two smaller angle,s therefore,

$x+y+90=180$

Step 2. Forming the equation

The measure of one of the

small angles of a right triangle is

14 more than 3 times the measure

of the other small angle.

therefore,

$x=14+3y$

Step 3. Solving for y

Put the values of $x=14+3y$into

$$\begin{gathered} x+y+90=180 \\ 14+3y+y+90=180 \\ 14+4y=90 \\ 4y=76 \\ y=\frac{76}{4} \\ y=19 \end{gathered}$$

Step 4. Solving for x

Put the values of$y=19$into$$\begin{gathered} x=14+3y \\ x=14+3\left(19\right) \\ =71 \end{gathered}$$