To solve this problem, we need to understand the concept of vertically opposite angles. Vertically opposite angles are equal when two lines intersect. This is a fundamental property of intersecting lines in geometry.
- Given that two lines intersect, four angles are formed at the intersection.
- The problem states that one of the angles measures \(45^\circ\).
- Since vertically opposite angles are equal, the angle directly opposite the \(45^\circ\) angle must also measure \(45^\circ\).
Therefore, the measure of the other angle, which is vertically opposite to the given angle of \(45^\circ\), is also \(45^\circ\).
Conclusion: The measure of the other angle is \(45^\circ\), which is choice $45^\circ$ in the given options.
Similar Questions
- In a right triangle, one of the acute angles is $30^\circ$. What is the measure of the exterior angle at the right-angled vertex?
- If the angle subtended by arc AB at the center is $140^\circ$, what is the reflex angle made by this arc at the center?
- Two angles are complementary. The measure of one angle is 10 degrees more than three times the measure of the other angle. What is the measure of the smaller angle?
- When a transversal intersects two parallel lines, one of the alternate interior angles is 115°. What is the measure of the angle that lies opposite to it on the alternate interior side?
Two parallel lines are intersected by a transversal. If a pair of corresponding angles is formed, and one of the angles measures 130°, what is the measure of the other angle?
Important Questions from Lines and Angles
Two parallel lines are intersected by a transversal, the corresponding angles are:
If l, m, n are lines such that, l is parallel to n and m is parallel to n, then, ______
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
Two cars start from a point at the same time and travel on two different roads at right angles to each other. Their speed is 18 km/h and 72 km/h respectively. What will be the distance between them after 6 seconds?
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
