Triangle Exterior Angles Worksheet - Practice Problems for Geometry Students

To solve the problems involving exterior angles of triangles, we need to use the Exterior Angle Theorem. This theorem states:

> The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent (remote) interior angles.

Part A: Solve for \( x \) in each triangle and find the measure of the indicated angle.

#### Problem 1:
[Diagram: Triangle with interior angles \( 40^\circ \) and \( 50^\circ \), and an exterior angle labeled \( x \).]

1. Identify the two non-adjacent interior angles: \( 40^\circ \) and \( 50^\circ \).
2. Use the Exterior Angle Theorem:
\[
x = 40^\circ + 50^\circ
\]
3. Calculate:
\[
x = 90^\circ
\]

#### Problem 2:
[Diagram: Triangle with interior angles \( 60^\circ \) and \( 70^\circ \), and an exterior angle labeled \( x \).]

1. Identify the two non-adjacent interior angles: \( 60^\circ \) and \( 70^\circ \).
2. Use the Exterior Angle Theorem:
\[
x = 60^\circ + 70^\circ
\]
3. Calculate:
\[
x = 130^\circ
\]

#### Problem 3:
[Diagram: Triangle with interior angles \( 30^\circ \) and \( 80^\circ \), and an exterior angle labeled \( x \).]

1. Identify the two non-adjacent interior angles: \( 30^\circ \) and \( 80^\circ \).
2. Use the Exterior Angle Theorem:
\[
x = 30^\circ + 80^\circ
\]
3. Calculate:
\[
x = 110^\circ
\]

Part B: Solve for \( x \) in each triangle and find the measure of the indicated angle.

#### Problem 1:
[Diagram: Triangle with one interior angle \( 50^\circ \), another interior angle \( x \), and an exterior angle \( 120^\circ \).]

1. Use the Exterior Angle Theorem:
\[
120^\circ = 50^\circ + x
\]
2. Solve for \( x \):
\[
x = 120^\circ - 50^\circ
\]
3. Calculate:
\[
x = 70^\circ
\]

#### Problem 2:
[Diagram: Triangle with one interior angle \( 45^\circ \), another interior angle \( x \), and an exterior angle \( 110^\circ \).]

1. Use the Exterior Angle Theorem:
\[
110^\circ = 45^\circ + x
\]
2. Solve for \( x \):
\[
x = 110^\circ - 45^\circ
\]
3. Calculate:
\[
x = 65^\circ
\]

#### Problem 3:
[Diagram: Triangle with one interior angle \( 60^\circ \), another interior angle \( x \), and an exterior angle \( 100^\circ \).]

1. Use the Exterior Angle Theorem:
\[
100^\circ = 60^\circ + x
\]
2. Solve for \( x \):
\[
x = 100^\circ - 60^\circ
\]
3. Calculate:
\[
x = 40^\circ
\]

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Part A:} & 90^\circ, 130^\circ, 110^\circ \\
\text{Part B:} & 70^\circ, 65^\circ, 40^\circ
\end{array}
}
\]