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 mAD=115° m Modifying above upper A upper D with arc equals 115 degrees mADC=84.5° m Modifying above upper A upper D upper C with arc equals 84.5 degrees m∠D=169°
Answers
Answer
what would be the best answer then?
Answered by
GPT-4o mini
To analyze the quadrilateral ABCD inscribed in a circle (also known as a cyclic quadrilateral), we can utilize some properties of cyclic quadrilaterals and the angles given.
1. **Sums of Opposite Angles**: The sum of the measures of opposite angles in a cyclic quadrilateral is \(180^\circ\).
Given that:
- m∠AB = 54°
- m∠BC = 115°
- m∠CD = 86°
We can find m∠AD using the fact that:
- m∠A + m∠C = 180°
- m∠B + m∠D = 180°
Let's first calculate m∠B:
Since we have:
- m∠B + m∠D = 180°
To find m∠D, we will first need to determine m∠A (which is equal to mAB):
1. **Finding m∠A**: Starting with the angle provided:
- m∠A = 54°
Now, using the property of opposite angles:
- m∠C = m∠B + m∠D
- 115° + m∠D = 180°
- m∠D = 180° - 115° = 65°
Next, we will find mADC:
Using:
- m∠D + m∠C = 180°
- 65° + 86° = 180°
Now that we have not calculated m∠B correctly, we will understand that when we look back we have given mAD instead of mD.
Thus summarily,
- m∠B = 115° from previous counts
- mAC = 54° + 86° = 140°
After all modifications from summation, we can see that:
1. m∠B = 95.5° is not correct
2. mAD = 120° not 115°
3. mADC = 84.5° is incorrect
4. m∠D= 169° does not fit the core sums observed of the quadrilateral.
Please adjust or recalculate exact angles using this outlined method above.
1. **Sums of Opposite Angles**: The sum of the measures of opposite angles in a cyclic quadrilateral is \(180^\circ\).
Given that:
- m∠AB = 54°
- m∠BC = 115°
- m∠CD = 86°
We can find m∠AD using the fact that:
- m∠A + m∠C = 180°
- m∠B + m∠D = 180°
Let's first calculate m∠B:
Since we have:
- m∠B + m∠D = 180°
To find m∠D, we will first need to determine m∠A (which is equal to mAB):
1. **Finding m∠A**: Starting with the angle provided:
- m∠A = 54°
Now, using the property of opposite angles:
- m∠C = m∠B + m∠D
- 115° + m∠D = 180°
- m∠D = 180° - 115° = 65°
Next, we will find mADC:
Using:
- m∠D + m∠C = 180°
- 65° + 86° = 180°
Now that we have not calculated m∠B correctly, we will understand that when we look back we have given mAD instead of mD.
Thus summarily,
- m∠B = 115° from previous counts
- mAC = 54° + 86° = 140°
After all modifications from summation, we can see that:
1. m∠B = 95.5° is not correct
2. mAD = 120° not 115°
3. mADC = 84.5° is incorrect
4. m∠D= 169° does not fit the core sums observed of the quadrilateral.
Please adjust or recalculate exact angles using this outlined method above.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.