Question

Quadrilateral cdef is inscribed in circle a. If mm∠c=7x+11 6m∠e=6x what is the measure?

a)29°
b)37°
c)41°
d)47°

Answer 1

The measure of angle c is 103 degrees.

Step-by-step explanation:

Quadrilateral cdef is inscribed in circle a, which means all its vertices lie on the circumference of the circle. In an inscribed quadrilateral, opposite angles are supplementary, which means they add up to 180 degrees. So, we have:

m∠c + m∠e = 180

Substituting the given values:

7x + 11 + 6x = 180

Combining like terms and solving for x:

13x + 11 = 180

13x = 169

x = 13

Now, substitute the value of x back into one of the equations to find the measure of ∠c:

m∠c = 7(13) + 11 = 92 + 11 = 103 degrees

Therefore, the measure of ∠c is 103 degrees. Option (c) - 41 degrees - is incorrect.