Angles Worksheets - Free Printable

To solve the problems involving the exterior angles of triangles, we need to use the Exterior Angle Theorem. The 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.

Let's go through each problem step by step.

---

Problem 1:

Find the measure of the indicated angle in each triangle.

#### (a)
Given:
- One interior angle = \(80^\circ\)
- Another interior angle = \(50^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = \text{Sum of the two non-adjacent interior angles}
\]
\[
\text{Exterior angle} = 80^\circ + 50^\circ = 130^\circ
\]

#### (b)
Given:
- One interior angle = \(70^\circ\)
- Another interior angle = \(60^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = 70^\circ + 60^\circ = 130^\circ
\]

#### (c)
Given:
- One interior angle = \(40^\circ\)
- Another interior angle = \(50^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = 40^\circ + 50^\circ = 90^\circ
\]

---

Problem 2:

Find the measure of the indicated angle in each triangle.

#### (a)
Given:
- One interior angle = \(60^\circ\)
- Another interior angle = \(70^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = 60^\circ + 70^\circ = 130^\circ
\]

#### (b)
Given:
- One interior angle = \(50^\circ\)
- Another interior angle = \(60^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = 50^\circ + 60^\circ = 110^\circ
\]

#### (c)
Given:
- One interior angle = \(30^\circ\)
- Another interior angle = \(40^\circ\)

We need to find the exterior angle adjacent to the third interior angle.

Using the Exterior Angle Theorem:
\[
\text{Exterior angle} = 30^\circ + 40^\circ = 70^\circ
\]

---

Final Answers:

1. (a) \(130^\circ\)
(b) \(130^\circ\)
(c) \(90^\circ\)

2. (a) \(130^\circ\)
(b) \(110^\circ\)
(c) \(70^\circ\)

\[
\boxed{
\begin{array}{ll}
1. & (a) 130^\circ, (b) 130^\circ, (c) 90^\circ \\
2. & (a) 130^\circ, (b) 110^\circ, (c) 70^\circ
\end{array}
}
\]