Question
Circle O is shown below
If m ∡ R = 28°, what is the m ∡ O?
a. 180°
b. 14°
c. 56°
d. 28°
If m ∡ R = 28°, what is the m ∡ O?
a. 180°
b. 14°
c. 56°
d. 28°
Answers
GPT-4o mini
To solve the problem, we need to understand the relationship between the angles in the circle and how they are related to each other.
Given that angle \( R \) measures \( 28^\circ \) and assuming that angle \( O \) refers to the angle formed at the center of the circle, we can use the inscribed angle theorem. This theorem states that the measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
If angle \( R \) is an inscribed angle and angle \( O \) is the corresponding central angle that subtends the same arc as angle \( R \), we can find the measure of angle \( O \) using the formula:
\[
m \angle O = 2 \times m \angle R
\]
Substituting the given value of \( m \angle R \):
\[
m \angle O = 2 \times 28^\circ = 56^\circ
\]
So the measure of angle \( O \) is \( 56^\circ \).
Hence, the answer is:
**c. 56°**
Given that angle \( R \) measures \( 28^\circ \) and assuming that angle \( O \) refers to the angle formed at the center of the circle, we can use the inscribed angle theorem. This theorem states that the measure of an inscribed angle is half the measure of the central angle that subtends the same arc.
If angle \( R \) is an inscribed angle and angle \( O \) is the corresponding central angle that subtends the same arc as angle \( R \), we can find the measure of angle \( O \) using the formula:
\[
m \angle O = 2 \times m \angle R
\]
Substituting the given value of \( m \angle R \):
\[
m \angle O = 2 \times 28^\circ = 56^\circ
\]
So the measure of angle \( O \) is \( 56^\circ \).
Hence, the answer is:
**c. 56°**