Question

Please help ASAP. Quadrilateral CDEF is inscribed in circle A. If the m∠C = 7x + 11° and m∠E = 7x + 1°, what is the measure of ∠E?
A) 95
B) 99
C) 81
D) 85

Answer 1

Answer:

The answer is D

Step-by-step explanation:

∠C + ∠E = 180°(consecutive angles)

7x +11° + 7x + 1° = 180°

14x + 12° = 180°

14x = 168°

x = 12°

∠E = 7x + 1°

= 7(12°) + 1

= 85°

Answer 2

Since angle C and angle E are opposite to each other and C and E are vertices of a cyclic quadrilateral,

m∠C + m∠E = 180°

7x + 11° + 7x + 1° = 180°

14x + 12° = 180°

14x = 168°

7x = 84°

∠E = 7x + 1°

∠E = 85°

Therefore, the answer is option D.

I hope this helps! If you have any doubts, feel free to ask.