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:
- Om<B = 95.5°: False (m∠B is 115°).
- Om<D = 169°: False (m∠ D is 40°, not 169°).
- O mAD = 115°: False (m∠AD is 65°, not 115°).
- 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.
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