Question
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∠D=169°
m angle upper D equals 169 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∠B=95.5°
Answers
GPT-4o mini
To solve for the angles in the inscribed quadrilateral ABCD, we can use the properties of cyclic quadrilaterals. The key property we utilize is that the sum of opposite angles in a cyclic quadrilateral equals 180 degrees.
Given:
- m∠A = 54°
- m∠B = 115°
- m∠C = 86°
We can find m∠D using the property that m∠A + m∠C = 180°.
First, we find m∠D:
1. Since m∠A + m∠C = 54° + 86° = 140°
2. Therefore, m∠D + m∠B = 180°
3. Substituting for m∠B:
- m∠D + 115° = 180°
- m∠D = 180° - 115° = 65°
Now, let’s check all the proposed options:
1. **m∠D = 169°**: (False, we found m∠D = 65°)
2. **mADC = 84.5°**: (There is not enough information to confirm as we are looking for angle ACD or CAD)
3. **mAD = 115°**: (False, as this option would not be accurate)
4. **m∠B = 95.5°**: (False, m∠B is given explicitly as 115°)
Now checking the calculations for m∠D from what we computed:
- Since m∠A + m∠C = 140°, thus m∠D + m∠B must equal 180°. We have m∠B = 115°, so 180 - 115 gives m∠D answering as 65°.
So none of the options are true based on the values and properties provided.
If there were assumptions or values missed please verify or provide more data, but if solely following cyclic quadrilateral properties, none of those suggested options hold.
The conclusion is that none of the selected statements are correct based on the provided values for the angles. Let me know if you have other questions!
Given:
- m∠A = 54°
- m∠B = 115°
- m∠C = 86°
We can find m∠D using the property that m∠A + m∠C = 180°.
First, we find m∠D:
1. Since m∠A + m∠C = 54° + 86° = 140°
2. Therefore, m∠D + m∠B = 180°
3. Substituting for m∠B:
- m∠D + 115° = 180°
- m∠D = 180° - 115° = 65°
Now, let’s check all the proposed options:
1. **m∠D = 169°**: (False, we found m∠D = 65°)
2. **mADC = 84.5°**: (There is not enough information to confirm as we are looking for angle ACD or CAD)
3. **mAD = 115°**: (False, as this option would not be accurate)
4. **m∠B = 95.5°**: (False, m∠B is given explicitly as 115°)
Now checking the calculations for m∠D from what we computed:
- Since m∠A + m∠C = 140°, thus m∠D + m∠B must equal 180°. We have m∠B = 115°, so 180 - 115 gives m∠D answering as 65°.
So none of the options are true based on the values and properties provided.
If there were assumptions or values missed please verify or provide more data, but if solely following cyclic quadrilateral properties, none of those suggested options hold.
The conclusion is that none of the selected statements are correct based on the provided values for the angles. Let me know if you have other questions!