Three angles have measures that add to 180° . The angles have the following measures: m∠KLM=(x+30)° , m∠MLN=60° , and m∠NLP=(2x)° . What is an equation to solve for the unknown angle measures? Write the equation in simplest terms.

Answer 1

The sum of the measures of the three angles is 180°.

Thus, we can write the equation as:

(x+30) + 60 + (2x) = 180

Simplifying the equation, we get:

3x + 90 = 180

Subtracting 90 from both sides:

3x = 90

Dividing both sides by 3:

x = 30

Therefore, the unknown angle measures are:

m∠KLM = (x+30) = 30 + 30 = 60°
m∠NLP = (2x) = 2(30) = 60°