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Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA. What is the measure of angle ADM?22.5°30.0°45.0°67.5°

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HomertheGenius
We know that ACD is an isosceles triangle.
Also angle CMA = 90° and it is the central angle.
Angle CDA is the peripheral angle:
∠ CDA = 90° : 2 = 45°
And the measure of angle ADM is half of the measure of angle CDA.
∠ ADM = 45° : 2 = 22.5°
Answer:
A ) 22.5°
MrRoyal

The measure of angle ADM is 22.5 degrees

From the figure, we have the following parameters:

  • [tex]\angle CMA = 90^o[/tex]

The angle at the center is twice the angle at the circumference.

So, we have:

  • [tex]2 \times \angle CDA = \angle CMA [/tex]

This gives

[tex]2 \times \angle CDA = 90[/tex]

Divide both sides by 2

[tex]\angle CDA = 45[/tex]

To calculate the measure of ADM, we make use of:

  • [tex]2 \times \angle ADM = \angle CDA[/tex]

So, we have:

[tex]2 \times \angle ADM = 45[/tex]

Divide both sides by 2

[tex]\angle ADM = 22.5^o[/tex]

Hence, the measure of angle ADM is 22.5 degrees

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