Question

AB || CD in the following figure. XY is the transversal. If m∠ PQA = 140°, find the measure of remaining angles

Answer 1

angle XQA +angle XQB =180( linear angle property )

angle XQB= 180°-140°

angle XQB= 40°

angle YQB=140°{ vertically opposite angle}

angle AQY=40°{ vertically opposite angle}

angle AQP=angle QPD= 140° (alternate interior angle)

angle CPX= angle QPD=140° (vertically opposite angel)

angle BQP=angle CPQ= 40° (alternate interior angle)

angle XPD=angle CPQ= 40° (V.O angles)

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Answer 2

$\huge{HEY!!}$
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⏩⏩In the following figure, we have been provided with only one angle which is ∠PQA .

∠XPD = ?
∠XPC = ?
∠DPQ = ?
∠CPQ = ?
∠PQB = ?
∠PQA = 140°
∠BQY = ?
∠AQY = ?

▶∠PQB = 40° (Angle Sum Property)
180° - 140° = 40°

▶∠BQY = 140° (Vertically Opposite Angle)

▶∠AQY = 40° (Vertically Opposite Angle)

▶∠DPQ = 140° (Alternate Interior Angles)

▶∠CPQ = 40° (Alternate Interior Angles)

▶∠XPD = 40° (Corresponding Angles)

▶∠XPC = 140° (Corresponding Angles)