The properties of parallel lines and corresponding angles, we can find that m∠y = 120° . Since PQ and RS are parallel, corresponding angles are congruent.
Given that line PQ and line RS are parallel, we can find the values of m∠x and m∠y using the following steps:
Identify the transversal: A transversal is a line that intersects two parallel lines. In this image, line XY is the transversal.
Identify corresponding angles: Corresponding angles are angles that lie on opposite sides of the transversal and between the two parallel lines.
In this case, ∠PXY and ∠SRY are corresponding angles.
Recognize the relationship between corresponding angles: Since PQ and RS are parallel, corresponding angles are congruent.
Therefore, m∠PXY = m∠SRY.
Find the measure of one angle: From the image, we can see that m∠PXY = 120°.
Substitute and solve for the other angle: Since m∠PXY = m∠SRY, we can substitute 120° for m∠SRY in the equation.
Therefore, m∠y = 120°.
Justification using geometry vocabulary:
Parallel lines: Lines PQ and RS are defined as parallel lines, meaning they never intersect no matter how far they are extended.
Transversal: Line XY intersects both PQ and RS, making it a transversal.
Corresponding angles: Angles PXY and SRY are corresponding angles because they lie on opposite sides of the transversal and between the two parallel lines.
Congruent angles: Since PQ and RS are parallel, corresponding angles are congruent. This is a fundamental property of parallel lines.
In conclusion, by using the properties of parallel lines and corresponding angles, we can find that m∠y = 120°.