📚 IGCSE Geometry Masterclass: Angles, Polygons and Circle Theorems | IGCSE几何精讲：角、多边形与圆定理
Welcome to TutorHao's IGCSE Mathematics revision guide. Geometry is a core component of the IGCSE syllabus, and mastering angle rules, polygon formulas and circle theorems can secure many marks in your exam. This article explains every key concept in a clear, bilingual way.
欢迎阅读 TutorHao 的 IGCSE 数学复习指南。几何是 IGCSE 考试大纲的核心内容，掌握角、多边形公式和圆定理可以为你在考试中稳稳拿分。本文将以清晰的中英双语方式讲解每一个关键概念。
1. Basic Angle Properties | 基本角性质
, if three angles around a point are 90°, 110° and x°, then x° = 360° − 90° − 110° = 160°.
一个点周围的角之和始终为 360°。这是许多图形题中用到的基本性质。例如，若一个点周围的三个角分别为 90°、110° 和 x°，则 x°=360°−90°−110°=160°。
Angles on a straight line sum to 180°. This rule is often combined with other rules to find missing angles in parallel-line and triangle questions.
直线上的角之和为 180°。该规则常与其它规则结合，用于求解平行线和三角形题中的未知角。
Vertically opposite angles are equal. When two straight lines intersect, the four angles formed have two pairs of equal angles. If one angle is 75°, the angle directly opposite is also 75°.
对顶角相等。当两条直线相交时，形成的四个角中有两对角分别相等。若一个角为 75°，其正对的角也为 75°。
Two angles are complementary when their sum is 90°. They are supplementary when their sum is 180°. These names appear regularly in exam questions and help you choose the correct calculation.
若两个角之和为 90°，则它们互为余角；若之和为 180°，则互为补角。这两个名称经常出现在考题中，有助于你选择正确的计算方法。
| Angle relationship | Rule |
| Angles at a point | sum = 360° |
| Angles on a straight line | sum = 180° |
| Vertically opposite angles | equal |
| Complementary angles | sum = 90° |
| Supplementary angles | sum = 180° |
The table above summarises the first five angle relations you must know.
上表总结了你必须掌握的前五种角关系。
2. Angles in Parallel Lines | 平行线中的角
When a transversal crosses two parallel lines, three important angle relationships appear. Alternate angles are equal. They form a Z shape. For example, if an alternate angle is 55°, the corresponding alternate angle is also 55°.
当一条截线穿过两条平行线时，会产生三种重要的角关系。内错角相等，形状像字母 Z。例如，若一个内错角为 55°，则另一个内错角也是 55°。
Corresponding angles are equal. They form an F shape. Corresponding angles lie on the same side of the transversal and in matching positions.
同位角相等，形状像字母 F。同位角位于截线同一侧，且位置对应。
Allied (co-interior)
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