To find the value of x, we first need to recognize that the angle formed by a chord and a tangent line is equal to half the measure of the intercepted arc.
In this case, the angle labeled x is formed by the chord AC and the tangent AD. So, we can find the measure of arc ACB, which is twice the measure of angle BAC.
Angle BAC is an inscribed angle that intercepts the same arc as angle ADC, which is subtended by x. So, the measure of angle BAC is equal to half of x, which is x/2.
Since angle BAC is equal to angle BCA (since triangle ABC is isosceles), they both have a measure of (180-38)/2 = 71 degrees.
So, the measure of arc ACB is twice the measure of angle BAC, which is 2*71 = 142 degrees.
Now, in circle O, the sum of the measures of all arcs together is 360 degrees. Since arc ACB is 142 degrees, arc AOB must be 360-142 = 218 degrees.
Therefore, the value of x is equal to the measure of arc ADC, which is 218 degrees. So, x = 218.
For the following question, assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x. The figures are not drawn to scale
58
38
44
218
1 answer