Question

........................................​

Answer 1

vii) x = 70° viii) x = 60°

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°

Answer 2

vii. x = 70° viii. x = 60°

Explanation:

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`]

⇒ 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°