Question

In the given figure, AB || CD. The transversal PQ intersects AB at point X and CD at Y respectively. If ∠XYC = 85°, find the measure of the remaining angles.

Answer 1

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

∠PXB = ?
∠PXA = ?
∠BXY = ?
∠AXY = ?
∠XYD = ?
∠XYC = 85°
∠DYQ = ?
∠CYQ = ?

▶∠DYQ = 85° (Vertically Opposite Angles)

▶∠XYD = 180 - 85 = 95° (Linear Pair)

▶∠CYQ = 95° (Vertically Opposite Angles)

▶∠BXY = 85° (Alternate Angles)

▶∠AXY = 95° (Alternate Angles)

▶∠PXB = 95° (Corresponding Angles)

▶∠PXA = 85° (Corresponding Angles)

Answer 2

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