Question
The m∠B is 86°, the measure of arc BC is 64°, and the measure of arc CD is 109°. Find the measure of <A. (1 point) Responses 86.5° 86.5° 64° 64° 94° 94° 93.5°
Answers
Answered by
GPT-4o mini
To find the measure of angle \( A \), we need to consider the properties of angles and arcs in a circle.
In a circle, the measure of an angle formed by two chords meeting at a point inside the circle can be found using the formula:
\[
m∠A = \frac{1}{2} \left( m \text{arc } BC + m \text{arc } CD \right)
\]
Given:
- \( m∠B = 86^\circ \) (this is not directly needed to find \( m∠A \))
- \( m \text{arc } BC = 64^\circ \)
- \( m \text{arc } CD = 109^\circ \)
Plugging in the values for the arcs:
\[
m∠A = \frac{1}{2} \left( 64^\circ + 109^\circ \right)
\]
Calculating the sum of the arcs:
\[
64^\circ + 109^\circ = 173^\circ
\]
Now, calculating the measure of angle \( A \):
\[
m∠A = \frac{1}{2} \times 173^\circ = 86.5^\circ
\]
Therefore, the measure of angle \( A \) is \( 86.5^\circ \).
**Answer: 86.5°**
In a circle, the measure of an angle formed by two chords meeting at a point inside the circle can be found using the formula:
\[
m∠A = \frac{1}{2} \left( m \text{arc } BC + m \text{arc } CD \right)
\]
Given:
- \( m∠B = 86^\circ \) (this is not directly needed to find \( m∠A \))
- \( m \text{arc } BC = 64^\circ \)
- \( m \text{arc } CD = 109^\circ \)
Plugging in the values for the arcs:
\[
m∠A = \frac{1}{2} \left( 64^\circ + 109^\circ \right)
\]
Calculating the sum of the arcs:
\[
64^\circ + 109^\circ = 173^\circ
\]
Now, calculating the measure of angle \( A \):
\[
m∠A = \frac{1}{2} \times 173^\circ = 86.5^\circ
\]
Therefore, the measure of angle \( A \) is \( 86.5^\circ \).
**Answer: 86.5°**