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


Question

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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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Dicussion (1)

  • 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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