Question

Plz help me ASAP! Thank you! Quadrilateral CDEF is inscribed in a circle A. If the m angle C = 7x + 11° and m angle E = 6x°, what is the measure of angle E?

78°
85°
95°
102°

Answer 1

Answer: 78°

Explanation:

First let’s solve for x

7x + 11 + 6x = 180°

13x + 11 = 180°

13x = 169

x = 13

plug in x in the equation 6x to solve for angle E

6(13) = 78°

that’s your answer :)

Answer 2

E = 78°.

Explanation:

One of the properties of the circles is that if there is a quadrilateral whose all corners lie on the circumference of the same circle, then the opposite angles of the quadrilateral are supplementary i.e. they sum up to 180°. In the quadrilateral CDEF, angles C and E are opposite angles. Since CDEF is inscribed in a circle, therefore their sum is 180°. Therefore:

Angle C + Angle E = 180°.

7x° + 11° + 6x° = 180°.

13x° = 169°.

x° = 13°.

Since E = 6x°, therefore E = 6(13°) = 78°.

Therefore, angle E measures 78 degrees!!!