Mathematics

Calculate the value of $$x$$ in each of the following figures.


SOLUTION
We know that in the triangle $$AEF$$ exterior angle is equal to the sum of two opposite interior angles

So we can write it as

$$\angle BED = \angle EAF + \angle EFA$$

By substituting the values

$$100^{\circ} = 40^{\circ} + \angle EFA$$

On further calculation

$$\angle EFA = 100^{\circ} - 40^{\circ}$$

By subtraction

$$\angle EFA = 60^{\circ}$$

From the figure we know that $$\angle CFD$$ and $$\angle EFA$$ are vertically opposite angles

So we get

$$\angle CFD = \angle EFA = 60^{\circ}$$

We know that in the triangle $$FCD$$ exterior angle is equal to the sum of two opposite interior angles

So we can write it as

$$\angle BCD = \angle CFD + \angle CDF$$

By substituting the values

$$90^{\circ} = 60^{\circ} + x^{\circ}$$

On further calculation

$$x^{\circ} = 90^{\circ} - 60^{\circ}$$

By subtraction

$$x^{\circ} = 30^{\circ}$$.
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Subjective Medium Published on 09th 09, 2020
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