Given circle E with diameter AC and m<DAC=62 degrees, find mAD(arc).
it's difficult to show solutions (because diagrams are required), but my answer is 58 degrees.
*i mean 56 degrees.
To find the measure of arc AD, we need to know the measure of the central angle that intercepts arc AD. From the given information, we know that angle DAC is 62 degrees.
In a circle, the measure of an arc is equal to the measure of its corresponding central angle. Therefore, to find the measure of arc AD, we need to determine the measure of the central angle that intercepts arc AD.
Since AC is the diameter of the circle, angle DAC is a right angle (90 degrees). This means that angle DAC is half of the central angle that intercepts arc AD, since it is inscribed in a semicircle.
Let's calculate the measure of the central angle that intercepts arc AD. Since angle DAC is 62 degrees, we can find the central angle by doubling this measure:
Central angle = 2 * angle DAC
Central angle = 2 * 62 degrees
Central angle = 124 degrees
Therefore, the measure of arc AD is also 124 degrees since they are equal to the measure of the corresponding central angle.