Final answer:
To find the measure of angle E, we set up an equation by considering that C and E must add up to 360 degrees in a circle. Solving the equation, we find that the measure of E is 160.75 degrees.
Step-by-step explanation:
To find the measure of E, we are given that the measure of C is 9x degrees and the measure of E is 7x + 4 degrees. Since C and E are angles in a circle, they must add up to 360 degrees. So we can set up the equation 9x + 7x + 4 = 360. Combining like terms, we get 16x + 4 = 360. Subtracting 4 from both sides, we have 16x = 356. Finally, dividing both sides by 16, we find that x = 22.25. To find the measure of E, we substitute this value back into the expression 7x + 4, giving us 7(22.25) + 4 = 156.75 + 4 = 160.75 degrees. Therefore, the measure of E is 160.75 degrees.