Answer: The value of 'x' is 31.
Step-by-step explanation: As shown in the modified attached figure, AC and BD are two intersecting chords, where ∠CBD = x° and ∠CAD = 31°.
We are to find the value of 'x'.
The measures of the angles on the circumference of a circle subtended by the same chord (arc) are equal.
In the attached figure, ∠CBD and ∠CAD are angles subtended at the circumference of the circle by the same arc CD.
Therefore, we must have
[tex]\angle CBD=\angle CAD\\\\\Rightarrow x^\circ=31^\circ.[/tex]
Therefore, the value of 'x' is 31.
Thus, (B) is the correct option.
