Question

In the diagram below, AB is a diameter of the circle. If arc CB measures 98 °, find the measure of < ABC.

Answer 1

In the figure, the missing angle, angle ABC is 41 degrees.

How to find the angle

Examining the figure, we can say that angle C is equal to 90 degrees.

And angle CAB and angle ABC are complementary angles.

To find angle CAB, we use the formula

Angle CAB = 1/2 arc CB

plugging in the values

Angle CAB = 1/2 ( 98 )

Angle CAB = 49.

Solving for angle ABC

angle CAB + angle ABC = 90

49 + angle ABC = 90

angle ABC = 90 - 49

angle ABC = 41 degrees

Answer 2

In this problem

arc ACB=180 degrees -----> because AB is a diameter

arc ACB=arc AC+ arc CB ----> by addition angles postulate

substitute given values

180=arc AC+98

arc AC=82 degrees

Find out the measure of angle mm by inscribed angle

mm

The answer is option A