If angle 3 is 30 degrees and angle 4 is a same-side interior angle, what is the

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Question: If angle 3 is 30 degrees and angle 4 is a same-side interior angle, what is the measure of angle 4 if the lines are parallel?

Options:

Correct Answer: 150 degrees

Solution:

Same-side interior angles are supplementary, so angle 4 measures 150 degrees.

If angle 3 is 30 degrees and angle 4 is a same-side interior angle, what is the measure of angle 4 if the lines are parallel?

If angle 3 is 30 degrees and angle 4 is a same-side interior angle, what is the measure of angle 4 if the lines are parallel?

Step 1: Identify that angle 3 is given as 30 degrees.
Step 2: Understand that angle 4 is a same-side interior angle to angle 3.
Step 3: Recall that same-side interior angles are supplementary when the lines are parallel, meaning they add up to 180 degrees.
Step 4: Set up the equation: angle 3 + angle 4 = 180 degrees.
Step 5: Substitute the value of angle 3 into the equation: 30 degrees + angle 4 = 180 degrees.
Step 6: Solve for angle 4 by subtracting 30 degrees from both sides: angle 4 = 180 degrees - 30 degrees.
Step 7: Calculate the result: angle 4 = 150 degrees.

Same-Side Interior Angles – When two parallel lines are cut by a transversal, the same-side interior angles are supplementary, meaning they add up to 180 degrees.
Supplementary Angles – Two angles are supplementary if their measures add up to 180 degrees.
Parallel Lines – Parallel lines are lines in a plane that do not meet; they are always the same distance apart.