Question
Two parallel lines are cut by a transversal.
The image depicts two parallel lines and one intersecting line across the parallel lines.
Text description for image
If the measure of ∠2 is 75°, what is the measure of ∠5?
A.
105°
B.
90°
C.
75°
D.
180°
The image depicts two parallel lines and one intersecting line across the parallel lines.
Text description for image
If the measure of ∠2 is 75°, what is the measure of ∠5?
A.
105°
B.
90°
C.
75°
D.
180°
Answers
Answered by
GPT-4o mini
To determine the measure of angle ∠5, we need to analyze the angles formed by the two parallel lines and the transversal.
Given that the measure of ∠2 is 75°, we can identify the relationships between the angles:
1. ∠2 is an interior angle formed on the same side of the transversal as ∠5. The angles on the same side of a transversal and between two parallel lines are called consecutive interior angles.
2. Consecutive interior angles are supplementary, meaning their measures add up to 180°.
Since ∠2 = 75°, we can find ∠5 using the following equation:
\[
∠2 + ∠5 = 180°
\]
Substituting the known value of ∠2:
\[
75° + ∠5 = 180°
\]
To isolate ∠5, subtract 75° from both sides:
\[
∠5 = 180° - 75°
\]
\[
∠5 = 105°
\]
Thus, the measure of ∠5 is **105°**.
The correct answer is **A. 105°**.
Given that the measure of ∠2 is 75°, we can identify the relationships between the angles:
1. ∠2 is an interior angle formed on the same side of the transversal as ∠5. The angles on the same side of a transversal and between two parallel lines are called consecutive interior angles.
2. Consecutive interior angles are supplementary, meaning their measures add up to 180°.
Since ∠2 = 75°, we can find ∠5 using the following equation:
\[
∠2 + ∠5 = 180°
\]
Substituting the known value of ∠2:
\[
75° + ∠5 = 180°
\]
To isolate ∠5, subtract 75° from both sides:
\[
∠5 = 180° - 75°
\]
\[
∠5 = 105°
\]
Thus, the measure of ∠5 is **105°**.
The correct answer is **A. 105°**.