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?
- 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 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
If angles of a triangle are in the ration of 2 : 3 : 4, then the measure of the smallest angle is:
In the triangle, if AB = AC and ∠ABC = 72°, then ∠BAC is:
The angles of a triangle are (8x - 15)°,(6x - 11)° and ( 4x – 10)°. What is the value of x ?
In a ΔABC, the bisectors of ∠B and ∠C meet at point O, inside the triangle. If ∠BOC = 122°, then the measure of ∠A is:
In ΔABC, D is a point on side BC such that ∠ADC = 2∠BAD. If ∠A = 80° and ∠C = 38°, then what is the measure of ∠ADB?
