Question

Quadrilateral ABCD
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

To solve for the measure of angle \( D \) in the inscribed quadrilateral \( ABCD \), we can use the property that the opposite angles in a cyclic quadrilateral add up to \( 180^\circ \).

Given:
- \( m\angle B = 4y + 27 \)
- \( m\angle D = y - 12 \)

Since \( \angle B \) and \( \angle D \) are opposite angles, we have:
\[
m\angle B + m\angle D = 180^\circ
\]

Substituting the expressions for \( m\angle B \) and \( m\angle D \):
\[
(4y + 27) + (y - 12) = 180
\]

Combining like terms:
\[
4y + y + 27 - 12 = 180
\]
\[
5y + 15 = 180
\]

Now, isolate \( y \):
\[
5y = 180 - 15
\]
\[
5y = 165
\]
\[
y = \frac{165}{5}
\]
\[
y = 33
\]

Now, substitute \( y \) back to find \( m\angle D \):
\[
m\angle D = y - 12 = 33 - 12 = 21
\]

Thus, the measure of angle \( D \) is:
\[
\boxed{21}
\]