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In the diagram above calculate the value of x


Question

In the diagram above calculate the value of x

Options

A) 60\(^{\circ}\)

B) 100\(^{\circ}\)

C) 120\(^{\circ}\)

D) 140\(^{\circ}\)

The correct answer is C.

Explanation:

p + 40\(^{\circ}\) = 100\(^{\circ}\) (exterior ∠ = sum of two interior opp ∠s)
p = 100\(^{\circ}\) - 40\(^{\circ}\)
P = 60\(^{\circ}\)
But q + p = 180\(^{\circ}\) (∠s on a straight line)
q + 60\(^{\circ}\)
q = 180\(^{\circ}\) - 60\(^{\circ}\)
q = 120\(^{\circ}\)
x = q (corresponding ∠)
∴x = 120\(^{\circ}\)

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Dicussion (1)

  • p + 40\(^{\circ}\) = 100\(^{\circ}\) (exterior ∠ = sum of two interior opp ∠s)
    p = 100\(^{\circ}\) - 40\(^{\circ}\)
    P = 60\(^{\circ}\)
    But q + p = 180\(^{\circ}\) (∠s on a straight line)
    q + 60\(^{\circ}\)
    q = 180\(^{\circ}\) - 60\(^{\circ}\)
    q = 120\(^{\circ}\)
    x = q (corresponding ∠)
    ∴x = 120\(^{\circ}\)

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