Question

what is the value of x? 100° 120° 130° 150°

Explanation:

Step1: Apply the polygon exterior angle sum formula

For a polygon formed by these angles (considering the angles around the "path" of the figure), the sum of exterior - like angles is \(360^{\circ}\). Let the given angles be \(140^{\circ}\), \(34^{\circ}\), \(56^{\circ}\), and \(x\). Then the equation is \(140 + 34+56 + x=360\).

Step2: Simplify the left - hand side

First, add \(34\) and \(56\): \(34 + 56=90\). Then the equation becomes \(140+90 + x=360\), and \(140 + 90=230\). So, \(230+x=360\).

Step3: Solve for \(x\)

Subtract \(230\) from both sides of the equation: \(x=360 - 230\).

Answer:

\(x = 130^{\circ}\), so the answer is \(130^{\circ}\) (the third option).