Question

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

Explanation:

Step1: Use the exterior - angle sum formula for a polygon formed by parallel lines

The formula for the sum of exterior angles of a polygon formed by parallel - line - like angles is \(a + b + c=d\), where \(a = 140^{\circ}\), \(b = 34^{\circ}\), \(c = 56^{\circ}\), and \(d=x\) (by the property of angles formed by parallel - like lines: the sum of the non - adjacent exterior angles equals the remote exterior angle).

$$140^{\circ}+34^{\circ}+56^{\circ}=x$$

Step2: Calculate the sum

First, add \(34^{\circ}\) and \(56^{\circ}\): \(34^{\circ}+56^{\circ}=90^{\circ}\).
Then, add \(140^{\circ}\) and \(90^{\circ}\): \(140^{\circ}+90^{\circ}=130^{\circ}\).

Answer:

\(130^{\circ}\)