Quadrilateral ABCD

Question

is inscribed in circle O
. The m∠B=4y+27
and m∠D=y−12
. Determine the m∠D
.(1 point)
m∠D=
°

Answer 1

m∠D = y - 12

Since ABCD is inscribed in circle O, opposite angles are supplementary:

m∠B + m∠D = 180
4y + 27 + y - 12 = 180
5y + 15 = 180
5y = 165
y = 33

Now plug in the value of y to find m∠D:

m∠D = y - 12
m∠D = 33 - 12
m∠D = 21

Therefore, m∠D = 21°.