Question

1. circle c is shown with diameters be and ad. the measure of angle bac is 35°. what is the measure, in degrees, of de? 2. circle t is shown, where the measure of angle rsv is 23°. what is the measure of arc rv?

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Step2: For the first problem

In circle \(C\), \(\angle BAC\) is an inscribed angle that intercepts arc \(BC\). Given \(\angle BAC = 35^{\circ}\), then the measure of arc \(BC\) is \(2\times\angle BAC=70^{\circ}\). Since \(BE\) and \(AD\) are diameters, \(\angle BCD = 90^{\circ}\) (angle inscribed in a semi - circle). The central angle corresponding to arc \(DE\) is equal to the central angle corresponding to arc \(BC\) (vertically opposite central angles). So the measure of arc \(DE\) is \(70^{\circ}\).

Step3: For the second problem

In circle \(T\), \(\angle RSV\) is an inscribed angle that intercepts arc \(RV\). By the inscribed - angle theorem, if \(\angle RSV=23^{\circ}\), then the measure of arc \(RV\) is \(2\times\angle RSV\).

Answer:

1. \(70\)
2. \(46\)