Given a triangle ABC, where AB=17, BC=25, and angle A=45 degrees, determine the measure of angle C rounded to the nearest
integer. Please use geometric methods rather than trigonometry to enhance understanding of the triangle's properties.

Angles softly blend,

Seventeen and twenty-five,

Secrets they will send.

Key Term | Description |
---|---|

Triangle ABC | A geometric figure consisting of three vertices (A, B, and C) connected by three sides (AB, BC, and AC). |

AB | The side of the triangle between vertices A and B, with a length of 17 units. |

BC | The side of the triangle between vertices B and C, with a length of 25 units. |

Angle A | The angle formed between sides AB and AC, measuring 45 degrees. |

Angle C | The angle opposite side AB, which is to be determined using geometric methods. |

Geometric Methods | Approaches to solving the problem based on the properties of shapes and their relationships, rather than using trigonometric formulas. |

Nearest Integer | The result of rounding the calculated measure of angle C to the closest whole number. |

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