Find the value of x for measure of modifying above upper A upper B with arc equals 27 degrees and measure of modifying above upper C upper D with arc equals 49 degrees. The figure is not drawn to scale.
A circle with center x and points D, C, B, and A is shown. Diameter DxB and chord AC intersect.
(1 point)
Responses
38°
38°
51.5°
51.5°
76°
76°
22°
To find the value of x, we need to use the property that the angle at the center of a circle is twice the angle at the circumference that subtends the same arc.
From the information provided, we know that the measure of arc AD is 49 degrees. Therefore, the angle at the center (x) of the circle is 2 * 49 = 98 degrees.
Similarly, the measure of arc AB is 27 degrees. Hence, the angle at the center (x) of the circle is 2 * 27 = 54 degrees.
Since the angle at the center (x) is formed by the intersection of diameter DxB and chord AC, we can set up an equation:
98 + 54 = 180 - x
152 = 180 - x
x = 180 - 152
x = 28 degrees
Therefore, the value of x is 28 degrees, which is closest to 22°.