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Quadrilateral ABCD is inscribed in a circle.

What is the measure of angle A?

Enter your answer in the box.

m∠A= [ ]°

flanspawn May 11, 2018

#1**+1 **

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. |

\(m\angle A=135^{\circ}\) |

TheXSquaredFactor May 11, 2018