+55 Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m∠A= [ ]°
+2446 The figure ABCD has four sides, and its vertices lie on a circle. This situation has a specific name: cyclic quadrilateral. This situation also has a specific theorem associated to it: Opposite angles of a cyclic quadrilateral are supplementary. Let's use this theorem to our advantage:
| \(m\angle A+m\angle C=180^{\circ}\) | Substitute in the known expressions for both of these angles. |
| \(3x+6+x+2=180\) | Now, simplify the left-hand side as much as possible. |
| \(4x+8=180\) | Now, use algebraic manipulation to isolate the variable. |
| \(4x=172\) | |
| \(x=43\) | Now, find the measure of the missing angle. |
| \(m\angle A=3x+6\) | Substitute in the known value for x. |
| \(m\angle A=3*43+6\) | Simplify. |
| \(m\angle A=135^{\circ}\) |
