Question

Use the inscribed angle rule to find the value of xin each circle. Show your work.

Answer 1

Answer:

Left: x = 56

Right: x = 58 1/2

Step-by-step explanation:

The inscribed angle theorem says that the inscribed angle subtended by an arc is half the measure of the central angle subtended by that same arc. In other words, if we had an arc with a measure of 12 degrees, its corresponding inscribed angle would be exactly 6 degrees, and if we had an inscribed angle measuring 10 degrees, it would be subtend an arc measuring 20 degrees.

On the left, we're given a measure of 28 degrees for the inscribed angle and have to find the measure of x, the subtended arc. Since 28 has to be half of x by the inscribed angle theorem, x must be 28 x 2 = 56°

On the right, we're given an arc with a measure of 117°, and we have to find the measure x° of the inscribed angle. Of course, this angle must be half of 117, so x = 117/2 = 58 1/2.