Question

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Answer 1

See below ~

Explanation:

a)

• 80 + 70 + y = 180 [co-interior angles are present]

• y + 150 = 180
• y = 30°

• x and 70° are alternate angles ⇒ x = 70°

b)

• y + 75 = 180° [Check line 1 of (a)]

• y = 105°

• x + y = 180°
• x + 105° = 180°
• x = 75°

c)

• 55° + 5x = 180° [Angle adjacent to 55° corresponds to (5x)°]

• 5x = 125°
• x = 25°

d)

• 64° + x = 180° [Check line 1 of (a)]

• x = 116°

Answer 2

a) - y = 30°,x = 70°

b)- y = 105°,x = 75°

c)- x = 25°

d)- x = 116°

Explanation:

a) =

80 + 70 + y = 180 (co-interior angles)

or, y = 180 - 150

so, y = 30°

Now,

x = 70° (alternate angles)

b) =

y + 75 = 180° (co-interior)

(y = angle which is supplement to 75)

y = 180° - 75°

so, y = 105°

Now,

x + y = 180° (co-interior angles)

or, x = 180° - 105°

so, x = 75°

c)=

180° - 5x = 55° (corresponding angles)

or, 5x = 180° - 55°

or, 5x = 125°

or, x = 125°/5

so, x = 25°

d)=

64° + x = 180° (co-interior angles)

x = 180° - 64°

so, x = 116°