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°

Answer 1

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.

Answer 2

what would be the best answer then?