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
- 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?
