Question

Points A, B, C, and D lie on circle M. Line segment BD is a diameter.

Triangle A C D is inscribed within circle M. Point B is on the circle between points C and B. A line is drawn to connect points D and B. Lines are drawn from points C and A to point M to form a right triangle. Arcs C D and A D are congruent.

What is the measure of angle ACD?

45.0°
67.5°
112.5°
135.0°

Answer 1

Given: A, B, C, and D lie on circle M, Line segment BD is a diameter.

To find:  The measure of angle ACD?

Solution:

• Now we know that the inscribed angle CDA measures 1/2(arc AC).

• And also we know that arc AC = 90 degree.

• Then:

                ang CDA = 90 / 2

                ang CDA = 45

• Now we know that triangle ACD is isosceles, so:

                ang ACD + ang CAD + ang CDA = 180 degree

• But ang ACD = ang CAD

• So,

                ang ACD + ang ACD + ang CDA = 180 degree

                ang ACD  = 180-45 / 2

                ang ACD   = 67.5 degree

Answer:

            So the measure of angle ACD is 67.5 degree.

Answer 2

Answer:

it's 67.5

Step-by-step explanation: