Question

Quadrilateral CDEF is inscribed in circle A. If the m∠C = 9x° and m∠E = 7x + 4°, what is the measure of ∠E?

Answer 1

81 degrees i got it right

Explanation:

Answer 2

m∠E = 81°

Explanation:

Quadrilateral CDEF is inscribed in a circle, therefore it is cyclic quadrilateral. Opposite angles of a cyclic quadrilateral are supplementary.

`\therefore m\angle C+m\angle E = 180\degree\\\therefore 9x +7x+4\degree = 180\degree\\\therefore 16x+4\degree = 180\degree\\\therefore 16x = 180\degree-4\degree\\\therefore 16x = 176\degree\\\therefore x = (176\degree)/(16)\\\therefore x =11\degree\\\\\because m\angle E =7x+4\degree\\\therefore m\angle E =7* 11\degree+4\degree\\\therefore m\angle E =77\degree+4\degree\\\huge{\boxed{\therefore m\angle E =81\degree}}`