Question

what is the value of x?
a 101
b 74
c 90
d 94

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). Here \(n=7\), so the sum is \((7 - 2)\times180^{\circ}=900^{\circ}\).

Step2: Set up the equation

We know one angle is \(90^{\circ}\) (the right - angle). Then \(140 + 136+x+142 + 150+148+90=900\).

Step3: Simplify the left - hand side

\(140+136 + 142+150+148+90+x=(140+136)+(142+150)+(148+90)+x=276+292+238+x\).
\(276+292+238+x=(276 + 292)+238+x=568+238+x=806+x\).

Step4: Solve for \(x\)

Since \(806+x = 900\), then \(x=900 - 806=94\).

Answer:

D. 94