∠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)

Question

___x°+___=180

Answer 1

Since ∠KLM and ∠MLP are supplementary angles, their measures add up to 180 degrees. We can express this relationship mathematically using the measures given.

The measures of the angles are:

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

Setting up the equation we have: \[ (x + 30) + (2x + 60) = 180 \]

Now we can simplify this:

1. Combine like terms: \(x + 2x + 30 + 60 = 180\)
2. This simplifies to \(3x + 90 = 180\)

Now we can isolate \(x\): \[ 3x + 90 = 180 \] Subtract 90 from both sides: \[ 3x = 90 \] Then divide by 3: \[ x = 30 \]

If we're asked to write the equation in the form ___x° + ___ = 180, we can rearrange it as: \[ 3x + 90 = 180 \]

So in simplest terms the answer is: \[ 3x + 90 = 180 \]