Question
page 6 of 6 Circles and Quadrilaterals Quick Check 4 of 54 of 5 Items Question Draw the following diagram: quadrilateral ABCD inscribed in circle E . The mAB=54° , mBC=115° , and mCD=86° . Select the true statement.(1 point) Responses m∠B=95.5° m angle upper B equals 95.5 degrees mADC=84.5° m Modifying above upper A upper D upper C with arc equals 84.5 degrees mAD=115° m Modifying above upper A upper D with arc equals 115 degrees m∠D=169° m angle upper D equals 169 degrees Skip to navigation
Answers
Answered by
GPT-4o mini
To solve the problem regarding the angles in the cyclic quadrilateral ABCD inscribed in circle E, we can use the property that the sum of the opposite angles in a cyclic quadrilateral is 180 degrees.
Given:
- \( m\angle A = 54^\circ \)
- \( m\angle B = 115^\circ \)
- \( m\angle C = 86^\circ \)
Now, we can find the measure of angle D using the property that \( m\angle A + m\angle C = 180^\circ \) and \( m\angle B + m\angle D = 180^\circ \).
1. First, let's find \( m\angle D \):
\[
m\angle D = 180^\circ - m\angle B = 180^\circ - 115^\circ = 65^\circ
\]
2. Now check \( m\angle B + m\angle D \):
\[
m\angle B + m\angle D = 115^\circ + 65^\circ = 180^\circ \quad \text{(which is correct)}
\]
3. Next, since we have the measures of angles A, B, C, and D, we can verify:
- \( m\angle A + m\angle C = 54^\circ + 86^\circ = 140^\circ \) (not equal to 180°, which is okay)
- \( m\angle B + m\angle D = 115^\circ + 65^\circ = 180^\circ \)
The only angle we calculated correctly was \( m\angle D = 65^\circ \). Let’s summarize based on the properties and calculations.
Now let's evaluate the provided options:
- \( m\angle D = 169^\circ \) is incorrect based on our calculation.
- \( m\angle A + m\angle C = 54 + 86 = 140 \), not equal to 84.5 or any of the other incorrect options.
- Since we calculated \( m\angle D \) based on the properties, we confirm that none of the proposed angles directly match our calculations unless there are more angles specified or further ways to calculate the arc measures absent.
Make sure to double-check your angles and any specific conditions that could contribute to the measures. In this case, with \( D \) calculated as 65°, no responses apply, indicating it might need a rule-based review or a specific angle selection technique for final answers.
Based on established calculations, \( m\angle A + m\angle D \neq 180\) so you should use your understanding of cyclic properties to filter proposed answers.
Given:
- \( m\angle A = 54^\circ \)
- \( m\angle B = 115^\circ \)
- \( m\angle C = 86^\circ \)
Now, we can find the measure of angle D using the property that \( m\angle A + m\angle C = 180^\circ \) and \( m\angle B + m\angle D = 180^\circ \).
1. First, let's find \( m\angle D \):
\[
m\angle D = 180^\circ - m\angle B = 180^\circ - 115^\circ = 65^\circ
\]
2. Now check \( m\angle B + m\angle D \):
\[
m\angle B + m\angle D = 115^\circ + 65^\circ = 180^\circ \quad \text{(which is correct)}
\]
3. Next, since we have the measures of angles A, B, C, and D, we can verify:
- \( m\angle A + m\angle C = 54^\circ + 86^\circ = 140^\circ \) (not equal to 180°, which is okay)
- \( m\angle B + m\angle D = 115^\circ + 65^\circ = 180^\circ \)
The only angle we calculated correctly was \( m\angle D = 65^\circ \). Let’s summarize based on the properties and calculations.
Now let's evaluate the provided options:
- \( m\angle D = 169^\circ \) is incorrect based on our calculation.
- \( m\angle A + m\angle C = 54 + 86 = 140 \), not equal to 84.5 or any of the other incorrect options.
- Since we calculated \( m\angle D \) based on the properties, we confirm that none of the proposed angles directly match our calculations unless there are more angles specified or further ways to calculate the arc measures absent.
Make sure to double-check your angles and any specific conditions that could contribute to the measures. In this case, with \( D \) calculated as 65°, no responses apply, indicating it might need a rule-based review or a specific angle selection technique for final answers.
Based on established calculations, \( m\angle A + m\angle D \neq 180\) so you should use your understanding of cyclic properties to filter proposed answers.
There are no human answers yet. A form for humans to post answers is coming very soon!