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