measure of modifying above upper D upper E with arc equals 123 degrees and measure of modifying above upper B upper C with arc equals 55 degrees. Find measure of angle upper A.
The figure is not drawn to scale.
A circle with points D, C, B, and E is shown. Point A is outside of the circle. Lines D B A and E C A are shown.
34°
95.5°
68°
89°
To solve this problem, we can use the property that the measure of an angle formed by two secants intersecting outside a circle is equal to half the difference of the measures of the intercepted arcs.
Given that the measure of arc DE is 123 degrees and the measure of arc BC is 55 degrees, we can calculate the measure of angle A as follows:
Measure of angle A = 1/2 * (Measure of arc DE - Measure of arc BC)
Measure of angle A = 1/2 * (123 - 55)
Measure of angle A = 1/2 * 68
Measure of angle A = 34 degrees
Therefore, the measure of angle A is 34 degrees. The correct answer is the first option: 34°.