If ABCDE is a regular pentagon, what is the value of x in the figure above?
A. 36
B. 42
C. 45
D. 48
E. 72
The OA is A.
Please, can any expert assist me with this PS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
Hi AAPL,
Let's take a look at your question.
ABCDE is a regular pentagon. We know that we can calculate the sum of interior angles of a regular polygon using the formula:
$$\left(n-2\right)\times180^o$$
Where n is the number of sides of the polygon.
For a regular pentagon n = 5.
Therefore, sum of interior angles of a pentagon will be:
$$=\left(5-2\right)\times180^o$$
$$=\left(3\right)\times180^o=540^o$$
Since there are five angles inside the pentagon, we can calculate the measure of each angle as:
$$=\frac{540^o}{5}=108^o$$
Now we can find the interior angles of the triangle FAE.
$$m\angle FEA=180^o-m\angle DEA$$
$$m\angle FEA=180^o-108^o=72^o$$
Similarly,
$$m\angle FAE=180^o-m\angle BAE$$
$$m\angle FAE=180^o-108^o=72^o$$
Now we can find the value of x.
We know that sum of interior angles of a triangle is 180 degree, therefore,
$$x^o=180^o-m\angle FEA-m\angle FAE$$
$$x^o=180^o-72^o-72^o$$
$$x^o=36^o$$
Therefore, Option
A is correct.
Hope it helps.
I am available if you'd like any follow up.
