Alternate Interior Angles Theorem
This problem involves understanding the properties of angles formed when a transversal intersects two parallel lines.
We are given that one of the alternate interior angles measures $115^\circ$.
The core geometric principle is the Alternate Interior Angles Theorem, which states: When a transversal intersects two parallel lines, the resulting alternate interior angles are congruent (equal in measure).
Angle Calculation
The question asks for the measure of the angle that lies "opposite to it on the alternate interior side". This phrasing refers to the other angle within the same pair of alternate interior angles.
- Given angle measure = $115^\circ$.
- According to the Alternate Interior Angles Theorem, the other angle in the alternate interior pair is equal to this given angle.
- Therefore, the measure of the angle opposite to it on the alternate interior side is also $115^\circ$.
Result
The measure of the specified angle is $115^\circ$.
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?
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?
- At an intersection of two lines, two angles are vertically opposite. If one of the angles measures $45^\circ$, 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:
