We want to find the measures of the angles in the given triangle.

To find these angle measures, we will first recall a key piece of information!

Angle Sum of a Triangle
The sum of the measures of the interior angles of a triangle is $18 0^{\circ} .$

With this rule, we can write an equation connecting the measures of the angles of our triangle.

2 x^{\circ} + 3 x^{\circ} + x^{\circ} = 18 0^{\circ}

Let's solve the equation and find the value of

x .

For simplicity, we will not write the degree symbol.

2 x + 3 x + x = 180

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Solve for

x

Add terms

6 x = 180

$LHS / 6 = RHS / 6$

x = 30

The measure of one of the angles is

3 0^{\circ} .

To find the other missing measures, we will substitute

x = 30

in the expressions for the remaining angles,

2 x^{\circ}

and

3 x^{\circ} .

Let's start with

2 x^{\circ} .

Once again, we will remove the degree symbol for the calculation.

2 x

$x = 30$

2 (30)

60

The measure of the second angle is

6 0^{\circ} .

Now, let's find the measure of

3 x^{\circ} .

3 x

$x = 30$

3 (30)

90

The measure of the third angle is

9 0^{\circ} .

Exercise