∠KLM and ∠MLP are supplementary angles. The angles have the following measures: m∠KLM=(x+30)° and m∠MLP=(2x+60)°. What is an equation to solve for the unknown angle measures? Write the equation in simplest terms. (1 point)

Since ∠KLM and ∠MLP are supplementary angles, their measures add up to 180 degrees. Therefore, the equation to solve for the unknown angle measures is:

m∠KLM + m∠MLP = 180°

Given that [tex] m\angle KLM = (x+30)^\circ [/tex] and [tex] m\angle MLP = (2x+60)^\circ [/tex], substitute these into the equation:

[tex] (x+30) + (2x+60) = 180 [/tex]

let's solve this:

Combine like terms:

[tex] 3x + 90 = 180 [/tex]

Now, solve for [tex] x [/tex]:

[tex] 3x = 90 [/tex]

[tex] x =\dfrac{90}{3}[/tex]

[tex] x = 30 [/tex]

Now that we have the value for [tex] x [/tex], you can substitute it back into the expressions for [tex] m\angle KLM [/tex] and [tex] m\angle MLP [/tex] to find their specific measures:

[tex] m\angle KLM = (30 + 30)^\circ = 60^\circ [/tex]

[tex] m\angle MLP = (2 \times 30 + 60)^\circ = 120^\circ [/tex]

So, the equation to solve for the unknown angle measures is [tex] 3x + 90 = 180 [/tex], and when solved, it gives [tex] x = 30 [/tex], [tex] m\angle KLM = 60^\circ [/tex], and [tex] m\angle MLP = 120^\circ [/tex].