这部分需要会什么？
- 使用对顶角、邻补角和平行线角关系
- 求三角形与多边形内角
- 把图中的角关系转为方程
核心概念与公式
对顶角相等，组成平角的邻角之和为 \(180^\circ\)，围绕一点的角之和为 \(360^\circ\)。两条平行线被截时，同位角和内错角相等，同旁内角互补。
三角形内角和为 \(180^\circ\)，一个外角等于不相邻两内角之和。\(n\) 边形内角和为 \((n-2)180^\circ\)；正 \(n\) 边形每个内角为该总和除以 \(n\)，每个外角为 \(360^\circ/n\)。
做题时怎样使用
- 先标出已知平行、垂直、等腰等条件
- 用最直接的角关系建立等式
- 算出角后检查它属于内角、外角还是补角，并确认大小合理
容易混淆的地方
只有给出或证明平行时，才能使用平行线的对应角关系；不能仅凭图看起来平行。多边形内角相等也需要正多边形等条件。
用一个例题串起方法
知识点教学例题三角形一个外角为 \(125^\circ\)，不相邻的两个内角分别为 \((2x+5)^\circ\) 和 \(3x^\circ\)。求 \(x\)。
展开解题思路 ＋
外角等于两不相邻内角之和，因此 \(2x+5+3x=125\)，得到 \(x=24\)。两个内角为 \(53^\circ\)、\(72^\circ\)，第三个为 \(55^\circ\)。
本知识点题库
先独立作答，再查看答案与解析。
直线・角与多边形进阶
In the figure, RT = TU, the measure of angle VST is 23° " , and the measure of angle RVS is 34° .What is the value of x ?
原库参考解析
直线・角与多边形进阶
In the figure shown, line r is parallel to line s, and both lines are intersected by line t. If x = 2w＋24, y =5w＋29, and 7w= a, where a is a constant, what is the value of a?
原库参考解析
直线・角与多边形进阶
In triangle ABC, the measure of angle A is 42° and the measure of angle B is 90 °. What is the measure, in degrees, of angle C?
原库参考解析
直线・角与多边形进阶
In the figure, line n intersects lines r and s. Line r is parallel to line s. What is the value of x?
原库参考解析
直线・角与多边形挑战
In triangle PQR, \( QR \) is extended to point S. The measure of ∠PQR is 132°, and the measure of ∠PRS is 166°. What is the measure of ∠QPR?
原库参考解析
直线・角与多边形进阶
In the figure, line n intersects lines r and s. Line r is parallel to line s. What is the value of x ?
原库参考解析
直线・角与多边形挑战
In triangle PQR, the measure of angle P is\( (4x+9)° \), the measure of angle Q is\( (5x+4)°, \)and the measure of angle R is\( (5y+4)°. \) If side QR is extended through point R to point S, and the measure of angle PRS is \( (x+y)° \) , what is the value of x+y?
原库参考解析
直线・角与多边形挑战
In the figure, parallel lines r and s are intersected by lines t, u, and w. If d = 64, g = 121, and h > d, which statement about j and p must be true?
原库参考解析
直线・角与多边形进阶
In the figure shown, line k intersects lines r and s, if w = 160, which additional piece of information is sufficient to prove that lines r and s are parallel?
原库参考解析
直线・角与多边形进阶
In the figure, two lines intersect at a point. If \( w=112 \). What is the value of z?
原库参考解析
直线・角与多边形进阶
In triangle \( RST \) , the measure of angle \( R \) is 39°, the measure of angle \( S \) is x°, and the measure of angle \( T \) is \( \left(5x-3\right)° \). Point \( L \) lies on \( RS \), point \( K \) lies on \( ST \) , and \( LK \) is parallel to \( RT \) . What is the measure, in degrees, of angle \( SKL \)? (Disregard the degree symbol when entering your answer.)
原库参考解析
直线・角与多边形进阶
In \( \triangle JKL \) , the measures of both \( ∠J \) and \( ∠K \) are equal and the measure of \( ∠L \) is \( 124° \). What is the measure of \( ∠J \) ?
原库参考解析
