Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Enter your answer in the box.
°
A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 2 x minus 40 right parenthesis degrees. The angle B is labeled as 116 degrees. The angle D is labeled as x degrees.
Answers
Step-by-step explanation:
The measure of angle B is 132°
Step-by-step explanation:
given : Quadrilateral ABCD is inscribed in this circle
\begin{gathered}\angle B = (3x-12) \\\\\angle D = x\end{gathered}
∠B=(3x−12)
∠D=x
we need to find the angle B
solution :
since we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees
therefore
in quadrilateral ABCD
\begin{gathered}\angle B + \angle D = 180^\circ\\\\3x-12 +x=180\\\\4x= 180+12\\\\4x=192\\\\x=\frac{192}{4}\\\\ x= 48^\circ\end{gathered}
∠B+∠D=180
∘
3x−12+x=180
4x=180+12
4x=192
x=
4
192
x=48
∘
then place the value of x in angle B
\begin{gathered}\angle B = 3x-12\\\\x= 48^\circ \\\\\angle B = 3(48) -12\\\\\angle B = 144-12\\\\\angle B = 132^\circ\end{gathered}
∠B=3x−12
x=48
∘
∠B=3(48)−12
∠B=144−12
∠B=132
∘
hence , The measure of angle B is 132°
