ABCD is a quadrilateral inscribed in a circle, as shown below:
Circle O is shown with a quadrilateral ABCD inscribed inside it. Angle A is labeled x plus 16. Angle B is labeled x degrees. Angle C is labeled 6x minus 4. Angle D is labeled 2x plus 16.
What equation can be used to solve for angle C?
(x + 16) + (x) = 180
(x + 16) + (6x − 4) = 180***
(x + 16) − (2x + 16) = 180
(x + 16) + (x) = 90
ABCD is a quadrilateral inscribed in a circle, as shown below:
please help
What equation can be used to solve for angle A?
(x + 16) + (6x − 4) = 180
(x + 16) + (x) = 90
(x + 16) − (2x + 16) = 180
(x + 16) − (x) = 90
The equation that can be used to solve for angle C is:
(x + 16) + (6x − 4) = 180
The equation that can be used to solve for angle C is (x + 16) + (6x - 4) = 180.
To understand why this equation is used, let's consider some properties of an inscribed quadrilateral:
1. The sum of the opposite angles in an inscribed quadrilateral is always 180 degrees.
2. In a circle, the opposite angles are formed by intersecting chords or tangents.
Applying these properties to quadrilateral ABCD, the opposite angles are A and C, and B and D. Therefore, the sum of angles A and C should be equal to 180 degrees.
Since angle A is labeled (x + 16) and angle C is labeled (6x - 4), we can express this relationship as:
(x + 16) + (6x - 4) = 180
By solving this equation, we can determine the value of x, which can subsequently be used to find the value of angle C.