Question

what is the measure of ∠x?
select the best answer from the choices provided.
a. 50°
b. 180°
c. 210°
d. 230°

Explanation:

Step1: Calculate the sum of the three given angles

The sum of the three non - \(x\) angles in the figure (the three angles of the "incomplete" quadrilateral - like shape) is \(30^{\circ}+60^{\circ}+40^{\circ}=130^{\circ}\).

Step2: Use the full - circle concept

A full circle is \(360^{\circ}\). The angle \(x\) and the sum of the three non - \(x\) angles form a full circle. So, \(x = 360^{\circ}-(30^{\circ}+60^{\circ}+40^{\circ})\).

$$x=360^{\circ}-130^{\circ}=230^{\circ}$$

Answer:

D. \(230^{\circ}\)