Solve multistep geometry problems involving lines, angles, and triangles. | Lines, angles, and triangles | SAT Math

Chain one geometry rule into the next when a problem needs more than one step.

核心知识

Harder SAT geometry problems chain two or more rules together — for example, using parallel-line angle relationships to find an angle, then applying the triangle angle sum to find another.

深入理解

Rule: Multistep geometry problems ask you to chain one rule into the next.

Start with the angle or side you can find first.
Write that value on the diagram.
Use the new value to unlock the final unknown.

A labeled diagram matters here because the second step usually depends on the first.

分步讲解

Read the problem and label the diagram with all given information.
Identify the first relationship you can use (parallel lines, vertical angles, etc.).
Calculate the intermediate value and add it to the diagram.
Look for the next relationship that connects your intermediate value to the unknown.
Repeat until you reach the answer.

常见误解

Trying to solve in one equation when two separate steps are needed.
Skipping the diagram — working without a labeled figure leads to misidentified angles.
Forgetting a rule that applies (e.g., not noticing that two angles are supplementary).

题目

示例解析

In the figure, lines $𝑚$ and $𝑛$ are parallel. A transversal intersects them, creating an angle of $62 °$ at line $𝑚$ . A triangle is formed between the two parallel lines, and one of its other angles (at line $𝑛$ ) measures $45 °$ . What is the measure of the third angle of the triangle?

选择一个答案查看解析