Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, what is the measure of angle CBD? Answer choices: a) 70 degrees b) 20 degrees c) 120 degrees d) 140 degrees e) 40 degrees

BA and BD are radii of the circle, so triangle ABD is isosceles. Then angles BDA and BAD are congruent, and the remaining (central) angle ABD has measure

[tex]m\angle ABD=(180-2\cdot20)^\circ=140^\circ[/tex]

Angles ABD and CBD are supplementary, so

[tex]m\angle CBD=(180-140)^\circ=40^\circ[/tex]

and the answer is E.

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Vickynehra Vickynehra · Answer 2 · 2022-05-16T08:27:51+02:00

The measure of the angle CBD is 40°.

What is a circle?

A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

According to the given problem,

BA and BD are radii of the circle.

Triangle ABD is isosceles.

Angles BDA and BAD are congruent.

m∠ABD = (180 - 2*20)

= 140°

Angles ABD and CBD are supplementary, so,

∠CBD = 180 - 140

= 40°

Hence, the measure of the angle CBD is 40°.

Learn more about circles here: https://brainly.com/question/11833983

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