Question

In the circle below AB is a diameter suppose CB=46° and m

Answer 1

The measure of angle CBA is 44 degrees, and the measure of angle ACD is 58 degrees.

Finding the measure of angle CBA:

Given that line AB is a diameter, angle ACB is 90 degrees according to the Inscribed Angle Theorem, which states that an angle inscribed in a semicircle is a right angle. Therefore,

Angle CBA = Angle ACB - Angle CBO = 90 degrees - 46 degrees = 44 degrees.

So, the measure of angle CBA is 44 degrees.

Finding the measure of angle ACD:

Since angles ACD and BCD are intercepted by the same arc CD, they have equal measures. Thus,

Measure of angle ACD = Measure of angle BCD = 58 degrees.

So, the measure of angle ACD is 58 degrees.