Question

consecutive interior angles add up to: a. 360 degrees b. 90 degrees c. 120 degrees d. 180 degrees if two angles measure 2x + 10 and 3x + 5 and are supplementary, find x. a. 35 b. 25 c. 33 d. 20

Explanation:

Step1: Recall angle - sum property of consecutive interior angles

Consecutive interior angles are supplementary, which means they add up to 180 degrees.

Step2: Set up an equation for supplementary angles

If two angles \(2x + 10\) and \(3x+5\) are supplementary, then \((2x + 10)+(3x + 5)=180\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(2x+3x+10 + 5=180\), which gives \(5x+15 = 180\).

Step4: Solve for \(x\)

Subtract 15 from both sides: \(5x=180 - 15=165\). Then divide both sides by 5: \(x=\frac{165}{5}=33\).

Answer:

1. d. 180 degrees
2. c. 33