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2 answers:
<u>Answer:</u>
vii. x = 70° viii. x = 60°
<u>Step-by-step explanation:</u>
vii.
The purple line drawn is parallel to the lines PQ and ST.
∴ ∠ a + 130° = 180° [alternate angles]
⇒ ∠ a = 50°
x = a + 20° [Co-interior angles with angle ]
⇒ x = 50° + 20°
⇒ x = 70°
viii.
The yellow line drawn and the line AB are parallel.
∴ n° + 130° = 180° [Co-interior angles]
n = 50°
The green line and line DE are parallel.
∴ m° + 110° = 180° [Co-interior angles]
m = 70°
n + m + x = 180° [Angles on a straight line]
⇒ 50° + 70° + x = 180°
⇒ x = 60°
Answer:
vii) x = 70° viii) x = 60°
Step-by-step explanation:
Please refer to the attached photos for better understanding (Apologies for the terrible drawing.)
vii) Angle RSV + Angle RST = 180° (Sum of angles in a straight line)
Angle RSV + 130° = 180°
Angle RSV = 180° - 130°
= 50°
Angle RVS + Angle RSV + Angle SRV = 180° (Sum of angles in a triangle)
Angle RVS + 50°+ 20° = 180°
Angle RVS = 180° - 70° = 110°
Angle RVX + Angle RVS = 180° (Sum of angles in a straight line)
Angle RVX + 110° = 180°
Angle RVX = 180° - 110° = 70°
Angle x = Angle RVX = 70° (Corresponding Angles)
viii) Angle FDG + Angle CDE = 180° (Sum of angles in a straight line)
Angle FDG + 110° = 180°
Angle FDG = 180° - 110°
= 70°
Angle BGC = Angle FDG = 70° (Corresponding Angles)
Angle CBG + Angle ABC = 180° (Sum of angles in a straight line)
Angle CBG + 130° = 180°
Angle CBG = 180 - 130°
= 50°
Angle x + Angle CBG + Angle BGC = 180° (Sum of angles in a triangle)
Angle x + 50° + 70° = 180°
Angle x = 180° - 120° = 60°
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