Question

The largest two angles of a triangle are two and three times as large as the smallest angle. Find all three measures.

Short answer

The measures of angles of triangle are, $30°,60°$and $90°$.

Step-by-step solution

Step 1. Description of a step.

Let the smallest angle be x. Therefore, the other angles of a triangle, are 2x and 3x.

Step 2. Apply an angle sum theorem.

Consider a triangle, such that,

$$\begin{gathered} x+2x+3x=180 \\ 6x=180 \\ x=30 \end{gathered}$$

Step 3. Description of a step.

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

Therefore, the value of x is

$x=30$

Step 4. Description of a step.

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

$\begin{array}{c}2x=2\times 30\\ =60\end{array}$

Step 5. Description of a step.

Substitute 30 for x into 3x to find the measure of third angle.

$\begin{array}{c}3x=3\times 30\\ =90\end{array}$

Therefore, the measures of angles of triangle are, $30°,60°$and $90°$.