Question

the measure of arc ab is
the measure of angle aob is
the measure of angle bda is
25
50
57
155
98°
212°

Explanation:

Step1: Find the measure of arc AB

The sum of the measures of the arcs of a circle is 360°. Given one arc is 212° and another is 98°. So, arc AB = 360°-(212° + 98°)=50°.

Step2: Find the measure of angle AOB

The measure of a central - angle is equal to the measure of its intercepted arc. Since arc AB = 50°, angle AOB = 50°.

Step3: Find the measure of angle BDA

The measure of an inscribed - angle is half the measure of its intercepted arc. Arc AB is 50°, so angle BDA=$\frac{1}{2}\times$ arc AB = 25°.

Answer:

The measure of arc AB is 50°.
The measure of angle AOB is 50°.
The measure of angle BDA is 25°.