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Is a diameter of \(D\). If \(m \angle BDC = 150°\), what is the measure of \(\angle \)?

A. 30°

B. 150°

C. 180°

D. 210°

1 Answer

0 votes

Final answer:

The measure of the angle at the circumference of a circle standing on the diameter is half the measure of the angle at the center.

Assuming m ∡ BDC = 150° represents the angle at the center formed by a diameter, the angle at the circumference (∡ A) would be 90°. This does not match the given options, suggesting possible missing details in the question.

Step-by-step explanation:

The student has given a geometry problem where the measure of an angle in a circle is to be found. Given that m ∡ BDC = 150°, and assuming BDC is an angle that intercepts a diameter, the measure of the angle at the circumference of the circle standing on that diameter would be half of 180°. This is because the angle at the center of the circle formed by a diameter is always a straight angle, which is 180°, and the angle at the circumference would be half of this according to the inscribed angle theorem.

Therefore, the measure of ∡ A would be:

  • (1/2) × 180° = 90°

However, since this answer is not in the options provided and the information seems incomplete or unclear, it seems there might be a missing detail or typo. With available information, a precise answer cannot be given to match the provided options.

User Manjunath Reddy
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