Question

In the given figure, AB II CD. Find the value of x.
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Answer 1

Answer: 20°

Step-by-step explanation:

AB ║ CD

∠PEA = 85°

∠PEA = ∠PGC = 85° (∵ Corresponding angles)

∠QGC = 180° - 85° = 95° (∵ Linear Pair)

∠CHQ = 115°

∠DHQ = 180° - 115° = 65° (∵ Linear Pair)

∴ ∠QGC = 95° ; ∠DHQ = 65°

∠QGC + ∠DHQ + ∠PQR = 180° (∵ Angle Sum Property)

95° + 65° + x = 180°

160° + x = 180°

x = 180° - 160°

x = 20°

∴ ∠PQR = 20°