5.1: Interior & Exterior Angles

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Geometry, Chapter 4, Lesson 1.

Problem 1 – Interior angles of a triangle

1. Record the measures of the interior angles of your triangle.

ABC\begin{align*}\angle{ABC}\end{align*} BCA\begin{align*}\angle{BCA}\end{align*} CAB\begin{align*}\angle{CAB}\end{align*}

2. What is the sum of the measures of the three interior angles of the triangle?

3. Does this result change when a vertex of the triangle is dragged?

Problem 2 – One exterior angle of a triangle

4. Record the measures of the interior angles and exterior angle BCD\begin{align*}\angle{BCD}\end{align*} of your triangle.

ABC\begin{align*}\angle{ABC}\end{align*} BCA\begin{align*}\angle{BCA}\end{align*} CAB\begin{align*}\angle{CAB}\end{align*} BCD\begin{align*}\angle{BCD}\end{align*}

5. Make some observations about the exterior angle BCD\begin{align*}\angle{BCD}\end{align*} and its relationship to other angles in the chart.

Problem 3 – Three exterior angles of a triangle

6. List the measures of the exterior angles of your triangle (one at each vertex).

Ext \begin{align*}\angle\end{align*} at vertex A\begin{align*}A\end{align*} Ext \begin{align*}\angle\end{align*} at vertex B\begin{align*}B\end{align*} Ext \begin{align*}\angle\end{align*} at vertex C\begin{align*}C\end{align*}

7. Calculate the sum of the three exterior angles.

8. Why do you think it is important to use one exterior angle at each vertex?

Find the missing angle measures in each of the diagrams below.

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