Calculate X and the marked angles.
We have hundreds of course questions with personalized recommendations + Account 100% premium
Calculate X and the marked angles.
Let us solve this step-by-step:
Step 1: Identify the angle relationship.
Since the angles are positioned on opposite sides of the transversal and between the two parallel lines, we can posit that these angles are alternate interior angles. These angles are equal when the lines are parallel.
Step 2: Set up the equation.
Since the alternate interior angles are equal, we set the expressions equal to one another:
Step 3: Solve the equation for .
Subtract from both sides to get: which simplifies to: Add to both sides to find:
The value of calculated is consistent with the nature of the angle relationships in parallel lines cut by a transversal.
Therefore, the solution to the problem is .
14
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
Look for angles on opposite sides of the transversal (crossing line) and between the parallel lines. They form a "Z" pattern when you trace from one angle to the other.
If lines aren't parallel, alternate interior angles are not equal! The problem usually tells you or shows parallel marks. When in doubt, assume they're parallel if angle expressions are given.
Alternate interior angles are congruent (equal), not supplementary. Only adjacent angles on a line add to 180°. These angles are in different positions, so they're equal.
Move variables to one side: , which gives . Always collect like terms and isolate the variable!
Substitute X = 14: First angle = , Second angle = . Both angles measure 19 degrees.
Get unlimited access to all 18 Parallel and Perpendicular Lines questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime