Answered

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An inscribed angle in a semicircle is always:

A. 45°
B. 90°
C. 180°
D. 360°

Sagot :

GinnyAnswer
To solve this problem, we need to understand some properties of circles and angles.

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint. This common endpoint is the vertex of the angle, and the other two endpoints define an arc on the circle.

When an angle is inscribed in a semicircle, the arc it intercepts spans a semicircle, which is half of the circle. A crucial theorem in circle geometry states that an angle inscribed in a semicircle is always a right angle.

Here's why:
- A semicircle is formed by a diameter of the circle.
- The diameter subtends an arc of 180°.
- An inscribed angle that intercepts this arc (the semicircle) must be half of 180°, which accordingly is 90°.

Therefore, the measure of an inscribed angle in a semicircle is always:

B. 90°
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