Question
Two parallel lines are intersected by a transversal. One of the angles formed measures \( 27^{\circ} \). What is the measurement of an adjacent angle? Enter your answer in the box.
Ask by Boyd Potter. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The adjacent angle measures \( 153^{\circ} \).
Solution
When two parallel lines are intersected by a transversal, several angles are formed. The angles that are adjacent to each other are supplementary, meaning they add up to \( 180^{\circ} \).
Given that one of the angles measures \( 27^{\circ} \), we can find the measurement of the adjacent angle by using the following formula:
\[
\text{Adjacent Angle} = 180^{\circ} - \text{Given Angle}
\]
Substituting the given angle:
\[
\text{Adjacent Angle} = 180^{\circ} - 27^{\circ}
\]
Now, let's calculate it:
\[
\text{Adjacent Angle} = 153^{\circ}
\]
Thus, the measurement of the adjacent angle is \( 153^{\circ} \).
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Simplify this solution The Deep Dive
When two parallel lines are intersected by a transversal, the angles formed have certain relationships. Adjacent angles formed by a transversal are supplementary, meaning they add up to \( 180^{\circ} \). Since one of the angles measures \( 27^{\circ} \), the measurement of the adjacent angle can be found by subtracting \( 27^{\circ} \) from \( 180^{\circ} \). So the calculation would be: \[ 180^{\circ} - 27^{\circ} = 153^{\circ} \] Thus, the measurement of the adjacent angle is \( 153^{\circ} \).
