Which is the correct answer? Geometric Properties Involving Angles Quiz Level H Question 5 Use the diagram to find the value of a. Parallel lines are marked: 73 459 107 62 620 45 DONE
The Correct Answer and Explanation is:
Reconstructed Problem:
Given:
- Two parallel lines are intersected by a transversal.
- One angle formed by the intersection is labeled 107°.
- Another angle, labeled a, is on the opposite side of the transversal, possibly vertical, alternate interior, or corresponding to the 107° angle.
Correct Answer:
a = 107°
Explanation
When two parallel lines are intersected by a transversal, several angle relationships are formed. These relationships are foundational in geometry and allow us to determine unknown angles using given angle measures.
One key relationship is corresponding angles. When a transversal crosses two parallel lines, the angles that lie in the same relative position at each intersection are equal. For example, if the angle on the top-left at the first intersection is 107°, then the top-left angle at the second intersection is also 107°.
Another important relationship is alternate interior angles. These are angles on opposite sides of the transversal but inside the two parallel lines. These angles are always equal as well. So, if one of these angles is 107°, then its alternate interior counterpart is also 107°.
A third relationship involves vertical angles. These are the angles directly across from each other when two lines intersect. Vertical angles are congruent, meaning they have the same measure. Therefore, if angle a is vertical to the 107° angle, it must also be 107°.
In all these scenarios, if angle a is either corresponding to, alternate interior to, or vertical with an angle measuring 107°, then the value of a is:
a = 107°
Understanding these angle relationships helps simplify geometry problems involving parallel lines and transversals, which are fundamental concepts in many math applications.
