Question

1. in the figure above, what is the value of x?

a. 70
b. 80
c. 110
d. 120

Explanation:

Step1: Find the sum of interior angles of a pentagon

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For \(n=5\), the sum is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Calculate the value of \(x\)

Let's assume the polygon \(ABCD\) (by adding a point \(A\), \(B\), \(C\), \(D\) and another non - labeled point). We know that the sum of angles around a point is \(360^{\circ}\). But if we consider the angles of the polygon - like structure.
We have \(30^{\circ}+(180 - 150)^{\circ}+(180 - 140)^{\circ}+x^{\circ}=360^{\circ}\) (using the property of angles in a non - standard polygon - like figure formed by extending sides).
First, \(180 - 150=30\) and \(180 - 140 = 40\).
Then \(30+30 + 40+x=360\).
\(100+x=360\).
\(x=360-(30 + 30+40)=120\).

Answer:

D. \(120\)