Question

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=
°
Remaini

Answer 1

In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of opposite angles equals \(180^\circ\).

In this case, we have:

\[
m\angle B + m\angle D = 180^\circ
\]

Given:

\[
m\angle B = 4y + 27
\]
\[
m\angle D = y - 12
\]

Set up the equation:

\[
(4y + 27) + (y - 12) = 180
\]

Combine like terms:

\[
4y + y + 27 - 12 = 180
\]
\[
5y + 15 = 180
\]

Now, isolate \(y\):

\[
5y = 180 - 15
\]
\[
5y = 165
\]
\[
y = \frac{165}{5} = 33
\]

Now, substitute \(y = 33\) back into the expression for \(m\angle D\):

\[
m\angle D = y - 12 = 33 - 12 = 21
\]

Thus,

\[
m\angle D = 21^\circ
\]

The measure of angle \(D\) is \(21^\circ\).