If two lines are cut by a transversal and the consecutive interior angles are 11

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Question: If two lines are cut by a transversal and the consecutive interior angles are 110 degrees and x degrees, what is the value of x?

Options:

Correct Answer: 70 degrees

Solution:

Consecutive interior angles are supplementary when two lines are parallel. Therefore, 110 + x = 180, so x = 70 degrees.

If two lines are cut by a transversal and the consecutive interior angles are 110 degrees and x degrees, what is the value of x?

If two lines are cut by a transversal and the consecutive interior angles are 110 degrees and x degrees, what is the value of x?

Step 1: Understand that consecutive interior angles are the angles that are on the same side of the transversal and between the two lines.
Step 2: Remember that if the two lines are parallel, consecutive interior angles add up to 180 degrees.
Step 3: Write down the equation for the angles: 110 degrees + x degrees = 180 degrees.
Step 4: To find x, subtract 110 degrees from both sides of the equation: x = 180 - 110.
Step 5: Calculate the result: x = 70 degrees.

Consecutive Interior Angles – Consecutive interior angles are pairs of angles that lie on the same side of the transversal and between the two lines. When the lines are parallel, these angles are supplementary, meaning their measures add up to 180 degrees.
Transversal – A transversal is a line that intersects two or more lines at distinct points. The properties of angles formed by a transversal are key in solving problems related to parallel lines.
Supplementary Angles – Supplementary angles are two angles whose measures add up to 180 degrees. This property is crucial when dealing with consecutive interior angles formed by a transversal.