Two parallel lines are cut by a transversal, creating angles of 75° and x°. What

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Question: Two parallel lines are cut by a transversal, creating angles of 75° and x°. What is the value of x?

Options:

Correct Answer: 105°

Solution:

The angles are supplementary, so x = 180° - 75° = 105°.

Two parallel lines are cut by a transversal, creating angles of 75° and x°. What is the value of x?

Two parallel lines are cut by a transversal, creating angles of 75° and x°. What is the value of x?

Step 1: Understand that two parallel lines cut by a transversal create pairs of angles.
Step 2: Identify the angles formed. In this case, we have one angle measuring 75° and another angle measuring x°.
Step 3: Recognize that the angles 75° and x° are supplementary, meaning they add up to 180°.
Step 4: Write the equation for supplementary angles: 75° + x° = 180°.
Step 5: To find x, subtract 75° from 180°: x = 180° - 75°.
Step 6: Calculate the result: x = 105°.

Supplementary Angles – When two angles add up to 180°, they are called supplementary angles. In this case, the angles formed by a transversal cutting parallel lines are supplementary.