SECTION C. SKILL-BASED QUESTIONS 1. In the given figure, find the values of x,y,z
Answers
Answer:
The value of z is:
= ∠OEB + 120° = 180° [Linear Pairs]
= ∠OEB = 180° - 120°
= ∠OEB = 60°
= ∠BOE = 60° [Vertically Opposite Angles]
= ∠OEB + ∠BOE + ∠OBE = 180° [Angle Sum Property Of Triangle]
= 60° + 60° + ∠OBE = 180°
= 120° + ∠OBE = 180°
= ∠OBE = 180° - 120°
= ∠OBE = 60°
= z + ∠OBE = 180 [Linear Pairs]
= z + 60° = 180°
= z = 180° - 60°
= z = 120°
Value of y is:
= ∠DOB + 60° = 180° [Linear Pairs]
= ∠DOB = 180° - 60°
= ∠DOB = 120°
= ∠DOB + z + 30 + y = 360 [Angle Sum Property]
= 120° + 120° + 30° + y = 360°
= 270° + y = 360°
= y = 360° - 270°
= y = 90°
Value of x is:
= ∠ODC + y = 180° [Linear Pair]
= ∠ODC + 90° = 180°
= ∠ODC = 180° - 90°
= ∠ODC = 90°
= ∠ODC + 60° + ∠DCO = 180° [Angle Sum Property]
= 90° + 60° + ∠DCO = 180°
= 150° + ∠DCO = 180°
= ∠DCO = 180° - 150°
= ∠DCO = 30°
= ∠DCO + x = 180°
= 30° + x = 180°
= x = 180° - 30°
= x = 150°