Question

what is the value of x in the figure shown below?
a) 32
b) 66
c) 82
d) 98

Explanation:

Step1: Identify similar triangles

Triangles $\triangle EAD$ and $\triangle CAB$ are similar because $\angle EAD=\angle CAB$ (vertically - opposite angles) and $\frac{EA}{CA}=\frac{DA}{BA}=\frac{5.1}{5.1}=\frac{4}{4} = 1$.

Step2: Use the property of similar - triangles for angle - equality

Since the triangles are similar, corresponding angles are equal. So, $\angle E=\angle C$ and $\angle D=\angle B$.
We know that in $\triangle CAB$, $\angle CAB = 32^{\circ}$ and $\angle B = 66^{\circ}$.
In $\triangle EAD$, we want to find $\angle E=x$.
Using the angle - sum property of a triangle ($\angle E+\angle D+\angle EAD = 180^{\circ}$). Since $\angle D=\angle B = 66^{\circ}$ and $\angle EAD=\angle CAB = 32^{\circ}$, we have $x+66^{\circ}+32^{\circ}=180^{\circ}$.

Step3: Solve for $x$

$x=180-(66 + 32)$
$x=180 - 98$
$x = 82^{\circ}$

Answer:

C. 82