Question

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Answer 1

Answer:

vii. x = 70°           viii. x = 60°

Step-by-step 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°

Answer 2

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°