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)
Om<B = 95.5°
Om<D = 169°
O mAD = 115°
O mADC = 84.5°

Answer 1

To solve this problem, we need to use the properties of cyclic quadrilaterals, specifically that opposite angles in a cyclic quadrilateral sum up to 180 degrees.

Let's denote the angles we know:
- m∠AB = 54°
- m∠BC = 115°
- m∠CD = 86°
- Let's denote m∠AD as x.

Using the property of cyclic quadrilaterals, we have:
- m∠AB + m∠CD = 180°, so:
m∠AB + m∠CD = 54° + 86° = 140°. Therefore, the measure of angle ∠DC is:
m∠DC = 180° - 140° = 40°.

Now we can find m∠AD using the measure of angle ∠BC:
- m∠BC + m∠AD = 180°, thus:
m∠BC + x = 180° = 115° + x = 180°.
Therefore, x = 180° - 115° = 65°.

So we have:
- m∠AD = 65°,
- m∠BC = 115°,
- m∠AB = 54°,
- m∠CD = 86°.

Now, let's analyze the true statements:
1. Om<B = 95.5°: False (m∠B is 115°).
2. Om<D = 169°: False (m∠ D is 40°, not 169°).
3. O mAD = 115°: False (m∠AD is 65°, not 115°).
4. O mADC = 84.5°: This notation might denote the measure of angle ∠ADC. From earlier, m∠ADC = 360° - (m∠AB + m∠BC + m∠CD) = 360° - (54° + 115° + 86°) = 360° - 255° = 105°.

Therefore, none of the provided options seem to represent accurate measures based on the previously discussed angles. Without further clarification on the notation or deeper examination, I would recommend reviewing the values given.

So in conclusion, based on the calculations, none of the statements provided are true.

Answer 2

make a guess please