Three angles have measures that add to 180°

Question

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.(1 point)

Answer 1

To solve for the unknown angle measures, we can set up an equation using the fact that the sum of the angle measures is 180°.

m∠KLM + m∠MLN + m∠NLP = 180°

We substitute the given measures into the equation:

(x+30)° + 60° + (2x)° = 180°

Combining like terms:

3x + 90° = 180°

Simplifying the equation:

3x = 90°

Dividing both sides by 3:

x = 30°

So the unknown angle measures are x+30°, 60°, and 2x° which simplify to:

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