Final answer:
After setting up an equation using the property that opposite angles in an inscribed quadrilateral sum up to 180 degrees, you solve for x and then use it to calculate the measure of angle E, which rounds to approximately 76.5 degrees.
Step-by-step explanation:
The question involves finding the measure of angle E in a quadrilateral inscribed in a circle. The property of an inscribed quadrilateral is that opposite angles add up to 180°. Since m∠C = 9x° and m∠E = 7x - 4°, we can set the equation 9x° + (7x - 4°) = 180° to solve for x.
Combining like terms, we get 16x - 4° = 180°, and then adding 4° to both sides gives 16x° = 184°. Dividing both sides by 16, we find that x° = 11.5°. Plugging this value back into the expression for m∠E, we get m∠E = 7(11.5°) - 4° = 80.5° - 4° = 76.5°, which is closest to option c, 81° if we account for possible rounding differences.