Question

The measure of one angle of a triangle is 28 more than the measure of the smallest angles of the triangle. The measure of the third angle is twice the measure of the smallest angle. Find all three measures.

Short answer

The measures of angles of triangle are, $38°,66°$and $76°$.

Step-by-step solution

Step 1. Description of a step.

Let the smallest angle be x. Therefore, the other angles of a triangle, are $x+28$and 2x.

Step 2. Apply an angle sum theorem.

Consider a triangle, such that,

$\begin{array}{c}x+x+28+2x=180\\ 4x=152\\ x=38\end{array}$

Step 3. Description of a step.

Substitute 38 for x into x to find the measure of first angle.

Therefore, the value of x is

$x=38$

Step 4. Description of a step.

Substitute 38 for x into$x+28$ to find the measure of second angle.

$\begin{array}{c}x+28=38+28\\ =66\end{array}$

Step 5. Description of a step.

Substitute 30 for x into 2x to find the measure of third angle.

$\begin{array}{c}2x=2\times 38\\ =76\end{array}$

Therefore, the measures of angles of triangle are, $38°66°$and $76°$.