Question

Quadrilateral cdef is inscribed in circle a. quadrilateral cdef is inscribed in circle a. if m∠def = (3x 7)° and m∠dcf = (2x 8)°, what is the value of x? 21 33 39 69

Answer 1

x = 33

Explanation:

a quadrilateral inscribed in a circle is a cyclic quadrilateral

the opposite angle of a cyclic quadrilateral sum to 180°

∠ def and ∠dcf are opposite angles , then

3x + 7 + 2x + 8 = 180

5x + 15 = 180 ( subtract 15 from both sides )

5x = 165 ( divide both sides by 5 )

x = 33