**In the diagram, MQ//RS, < TUV = 70° and < RLV = 30°. Find the value of x**

### Question

In the diagram, MQ//RS, < TUV = 70° and < RLV = 30°. Find the value of x

### Options

A) 150°

B) 110°

C) 100°

D) 95°

The correct answer is C.

### Explanation:

L + 30° - 180°(Sum of

L = 180° - 30° = 150°

L = q = 150° (opposite angles)

y = b = 30° (alternating angles)

b + c = 180° (sum of angles on a straight line)

30° + c = 180°

c = 180 - 30

c = 150°

b = a = 30° (opposite angles)

c = d = 150° (opposite angles)

a + k + 70° = 180° (sum of angles on a straight line)

30° + k + 70° = 180°

k + 100° = 180°

k = 180 - 100

k = 80°

x + 80° = 180(sum of angles on a straight line)

x = 180° - 80°

x = 100°

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L + 30° - 180°(Sum of

L = 180° - 30° = 150°

L = q = 150° (opposite angles)

y = b = 30° (alternating angles)

b + c = 180° (sum of angles on a straight line)

30° + c = 180°

c = 180 - 30

c = 150°

b = a = 30° (opposite angles)

c = d = 150° (opposite angles)

a + k + 70° = 180° (sum of angles on a straight line)

30° + k + 70° = 180°

k + 100° = 180°

k = 180 - 100

k = 80°

x + 80° = 180(sum of angles on a straight line)

x = 180° - 80°

x = 100°