In a circle, if a central angle measures 80 degrees, what is the measure of the

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Question: In a circle, if a central angle measures 80 degrees, what is the measure of the inscribed angle that subtends the same arc?

Options:

Correct Answer: 40 degrees

Solution:

The inscribed angle is half the measure of the central angle that subtends the same arc. Therefore, the inscribed angle measures 80/2 = 40 degrees.

In a circle, if a central angle measures 80 degrees, what is the measure of the inscribed angle that subtends the same arc?

In a circle, if a central angle measures 80 degrees, what is the measure of the inscribed angle that subtends the same arc?

Step 1: Understand that a central angle is an angle whose vertex is at the center of the circle and whose sides extend to the circumference.
Step 2: Recognize that an inscribed angle is an angle whose vertex is on the circumference of the circle and whose sides also extend to the circumference.
Step 3: Note that both the central angle and the inscribed angle subtend the same arc (the same part of the circle).
Step 4: Remember the rule: the inscribed angle is always half the measure of the central angle that subtends the same arc.
Step 5: Since the central angle measures 80 degrees, divide this by 2 to find the inscribed angle: 80 degrees / 2 = 40 degrees.
Step 6: Conclude that the measure of the inscribed angle is 40 degrees.

Inscribed Angles and Central Angles – The relationship between inscribed angles and central angles in a circle, where the inscribed angle is always half the measure of the central angle that subtends the same arc.