Which property of quadrilaterals inscribed in a circle can be used to find the value of x in the figure below?
The difference between an opposite pair of angles is 180°.
The difference between an opposite pair of angles is 0°.
The sum of an opposite pair of angles is 180°.
The sum of an opposite pair of angles is 360°
The property of quadrilaterals inscribed in a circle that can be used to find the value of x in the figure is "The sum of an opposite pair of angles is 180°."
To determine this, you can use the fact that for any quadrilateral inscribed in a circle, each pair of opposite angles are supplementary.
In the given figure, you can identify the pairs of opposite angles: Angle A and Angle C, and Angle B and Angle D.
If we know that Angle A and Angle C are supplementary, and the measure of Angle A is 50°, we can set up the equation:
Angle A + Angle C = 180°
Substituting the given value of Angle A, we have:
50° + Angle C = 180°
To find the value of x, we need to isolate Angle C. Therefore, we subtract 50° from both sides of the equation:
Angle C = 180° - 50°
Angle C = 130°
So the value of x is 130°.