Question

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

a. 95°
b. 99°
c. 81°
d. 85°

Answer 1

To find the measure of angle C and angle E, we need to set up an equation using the fact that the sum of angles in a quadrilateral is 360 degrees and that angles that are opposite each other in a circle are congruent.

Step-by-step explanation:

To find the measure of angle C and angle E, we need to set up an equation using the fact that the sum of angles in a quadrilateral is 360 degrees and that angles that are opposite each other in a circle are congruent.

m∠C + m∠E + m∠D + m∠F = 360

Since angles C and E are opposite each other in circle A, they are congruent.

9x + 7x + 4 + m∠D + m∠F = 360

Combining like terms, we have:

16x + 4 + m∠D + m∠F = 360

Subtracting 4 from both sides and simplifying, we get:

16x + m∠D + m∠F = 356

We cannot determine the exact measure of angles D and F without more information, so none of the answer choices are correct.