Final answer:
Using the property that opposite angles in an inscribed quadrilateral sum to 180 degrees, we first solve for x using given angle measures of A and C. Subsequently, we find m° B with x's value and then apply the property again to determine m° D, resulting in 98 degrees.
Step-by-step explanation:
The problem involves a quadrilateral inscribed in a circle, which refers to a property where opposite angles of the quadrilateral must sum to 180°. Given m° A is 64°, m° B is (6x + 4)°, and m° C is (9x - 1)°, we can find m° D by using the inscribed quadrilateral property.
- First, we know that m° A + m° C = 180° because they are opposite angles of an inscribed quadrilateral.
- Substituting the given measures, we have 64° + (9x - 1)° = 180°. Solving for x gives us x = 13°.
- Next, we calculate m° B using x by substituting 13 in the expression for m° B, so m° B = (6*13 + 4)° = 82°.
- Finally, because m° B and m° D are also opposite angles, we use the property again to find m° D: 180° - 82° = 98°.
Therefore, the measure of angle D, m° D, is 98°.