Question

points b and d are the endpoints of a diameter of the circle. how are the measures of arc ab and arc ad related? explain. which of the following is a correct response? because bd is a diameter, then dab is a circle. so, the sum of mab and mad will be 360. because bd is a diameter, then dab is a semicircle. so, the sum of mab and mad will be 360. because bd is a diameter, then dab is a circle. so, the sum of mab and mad will be 180. because bd is a diameter, then dab is a semicircle. so, the sum of mab and mad will be 180. show hints

Explanation:

Step1: Recall circle - arc property

A diameter of a circle divides the circle into two equal - parts called semicircles. The measure of a full - circle arc is 360°, and the measure of a semi - circle arc is 180°.

Step2: Analyze the arcs \(\overparen{AB}\) and \(\overparen{AD}\)

Since \(BD\) is a diameter, \(\overparen{DAB}\) is a semi - circle. The sum of the measures of \(\overparen{AB}\) and \(\overparen{AD}\) forms the semi - circle \(\overparen{DAB}\). So, \(m\overparen{AB}+m\overparen{AD}=180^{\circ}\).

Answer:

Because \(BD\) is a diameter, then \(\overparen{DAB}\) is a semi - circle. So, the sum of \(m\overparen{AB}\) and \(m\overparen{AD}\) will be \(180^{\circ}\).