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
- 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 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?
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?
- 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?
Important Questions from Lines and Angles
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?
Express 65° in radian :
The measure of an angle for which the measure of the supplement is four times the measure of the complement is:
AB||CD and EF is the transversal meeting AB and CD at P and Q, respectively. If ∠APE = 6x and ∠PQD = 4x, then ∠APQ =______.
