Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The adjacent angle measures \( 153^{\circ} \).
Solución
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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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 \( 153^{\circ} \).

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