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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$$^{\circ}$$

### 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$$^{\circ}$$

## 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$$^{\circ}$$