Question
The m∠B is 93°, the measure of arc BC is 58°, and the measure of arc CD is 106°. Find the measure of <C. (1 point) Responses 87° 87° 58° 58° 98° 98° 80°
Answers
Answered by
GPT-4o mini
To solve for the measure of angle \( C \) in this scenario, we can use the information provided about the arcs.
Given:
- \( m\angle B = 93^\circ \)
- \( m\) arc \( BC = 58^\circ \)
- \( m\) arc \( CD = 106^\circ \)
The measure of angle \( C \) can be found by using the property that the angle formed by two tangents or secants that meet outside the circle is half the difference of the measures of the arcs they intercept.
1. First, we identify which arcs correspond to angle \( C \). Assuming angle \( C \) intercepts arcs \( BC \) and \( CD \):
\[
m\angle C = \frac{m\text{ arc }CD - m\text{ arc }BC}{2}
\]
2. Plugging in the values:
\[
m\angle C = \frac{106^\circ - 58^\circ}{2} = \frac{48^\circ}{2} = 24^\circ
\]
3. This calculation may seem off as the angle \( C \) calculated at 24° is not listed in the options. Therefore, we need further clarification on which angles each label refers to.
However, if angle \( C \) is instead in fact the angle formed at point \( C \) by lines that extend to the circle (which can denote that arcs measure as their associated arcs),
we evaluate it as:
- If angle C intercepts arc BC and arc CD, which should be \( B \).
The appropriate angle should be:
\[
\frac{m\text{ arc }BCD + m\text{ arc }DCB}{2}
\]
Let’s interpret based on the tangents or inscribed angles and relevant point positioning if provided.
After checking:
- All angles are equal to respective intercepted degrees and confirming the structure:
### Given you can check via:
Since \( C\) is mostly involved in those calculation(s) will lead estimates and can yield either \( 87^\circ, and 98^\circ \) should relate the sum or mix.
The clarity is circled around assessments on how arcs reflect end intersections.
To take a step or another confirmation having those opts noted often places itself back to first or second based on direct angles thus leading towards clarifying further vastly beyond strict placement on \( C\) normally.
In summary:
The closest correct approach offers towards angle \( C\) bounds around \( 80-87\).
Based from prior valid arcs placements as reasoning; we derive 87° as the leading straightforward measure to angle \(C\).
Thus,
Final answer:
**87°**
Given:
- \( m\angle B = 93^\circ \)
- \( m\) arc \( BC = 58^\circ \)
- \( m\) arc \( CD = 106^\circ \)
The measure of angle \( C \) can be found by using the property that the angle formed by two tangents or secants that meet outside the circle is half the difference of the measures of the arcs they intercept.
1. First, we identify which arcs correspond to angle \( C \). Assuming angle \( C \) intercepts arcs \( BC \) and \( CD \):
\[
m\angle C = \frac{m\text{ arc }CD - m\text{ arc }BC}{2}
\]
2. Plugging in the values:
\[
m\angle C = \frac{106^\circ - 58^\circ}{2} = \frac{48^\circ}{2} = 24^\circ
\]
3. This calculation may seem off as the angle \( C \) calculated at 24° is not listed in the options. Therefore, we need further clarification on which angles each label refers to.
However, if angle \( C \) is instead in fact the angle formed at point \( C \) by lines that extend to the circle (which can denote that arcs measure as their associated arcs),
we evaluate it as:
- If angle C intercepts arc BC and arc CD, which should be \( B \).
The appropriate angle should be:
\[
\frac{m\text{ arc }BCD + m\text{ arc }DCB}{2}
\]
Let’s interpret based on the tangents or inscribed angles and relevant point positioning if provided.
After checking:
- All angles are equal to respective intercepted degrees and confirming the structure:
### Given you can check via:
Since \( C\) is mostly involved in those calculation(s) will lead estimates and can yield either \( 87^\circ, and 98^\circ \) should relate the sum or mix.
The clarity is circled around assessments on how arcs reflect end intersections.
To take a step or another confirmation having those opts noted often places itself back to first or second based on direct angles thus leading towards clarifying further vastly beyond strict placement on \( C\) normally.
In summary:
The closest correct approach offers towards angle \( C\) bounds around \( 80-87\).
Based from prior valid arcs placements as reasoning; we derive 87° as the leading straightforward measure to angle \(C\).
Thus,
Final answer:
**87°**
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