What is the value of X given that the angles are between parallel lines?
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What is the value of X given that the angles are between parallel lines?
The angle X given to us in the drawing corresponds to an angle that is adjacent to an angle equal to 154 degrees. Therefore, we will mark it with an X.
Now we can calculate:
26°
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
Adjacent angles on a straight line form what's called a linear pair. Since a straight line measures 180°, the two angles sharing that line must add up to 180°. Equal angles only occur with specific parallel line relationships like alternate interior angles.
Look at their position! Adjacent angles share a vertex and are next to each other on the same line. Alternate angles are on opposite sides of a transversal crossing parallel lines.
Parallel lines create multiple angle relationships! You might have corresponding angles (equal), alternate angles (equal), or co-interior angles (sum to 180°). Always identify the exact relationship first.
While you could subtract mentally (180 - 154 = 26), setting up the equation helps you organize your thinking and avoid calculation errors, especially with larger numbers.
Look at the position of the angles carefully. In this problem, X and 154° are clearly next to each other on the same straight line, making them a linear pair that must sum to 180°.
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