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

$x^{\circ} = 30^{\circ}$.

You're just one step away

Subjective Medium Published on 09th 09, 2020
Questions 120418
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