Exterior Angle Theorem interactive worksheet - Free Printable

To solve the problems using the Exterior Angle Theorem, we need to recall the following key points:

1. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.
2. Sum of Angles in a Triangle: The sum of the interior angles of a triangle is always \(180^\circ\).

Let's solve each problem step by step.

---

Problem 1:


Given:
- Two interior angles: \(58^\circ\) and \(58^\circ\).
- Exterior angle: \(h^\circ\).

Using the Exterior Angle Theorem:
\[
h = 58^\circ + 58^\circ = 116^\circ
\]

Answer:
\[
\boxed{116}
\]

---

Problem 2:


Given:
- One interior angle: \(82^\circ\).
- Another interior angle: \(32^\circ\).
- Exterior angle: \(b^\circ\).

Using the Exterior Angle Theorem:
\[
b = 82^\circ + 32^\circ = 114^\circ
\]

Answer:
\[
\boxed{114}
\]

---

Problem 3:


Given:
- One interior angle: \(k^\circ\).
- Another interior angle: \(90^\circ\) (right angle).
- Exterior angle: \(147^\circ\).

Using the Exterior Angle Theorem:
\[
147^\circ = k^\circ + 90^\circ
\]
Solving for \(k\):
\[
k = 147^\circ - 90^\circ = 57^\circ
\]

Answer:
\[
\boxed{57}
\]

---

Problem 4:


Given:
- One interior angle: \(56^\circ\).
- Another interior angle: \(90^\circ\) (right angle).
- Exterior angle: \(x^\circ\).

Using the Exterior Angle Theorem:
\[
x = 56^\circ + 90^\circ = 146^\circ
\]

Answer:
\[
\boxed{146}
\]

---

Problem 5:


Given:
- One interior angle: \(38^\circ\).
- Another interior angle: \(c^\circ\).
- Exterior angle: \(91^\circ\).

Using the Exterior Angle Theorem:
\[
91^\circ = 38^\circ + c^\circ
\]
Solving for \(c\):
\[
c = 91^\circ - 38^\circ = 53^\circ
\]

Answer:
\[
\boxed{53}
\]

---

Problem 6:


Given:
- One interior angle: \(n^\circ\).
- Another interior angle: \(90^\circ\) (right angle).
- Exterior angle: \(142^\circ\).

Using the Exterior Angle Theorem:
\[
142^\circ = n^\circ + 90^\circ
\]
Solving for \(n\):
\[
n = 142^\circ - 90^\circ = 52^\circ
\]

Answer:
\[
\boxed{52}
\]

---

Problem 7:


Given:
- One interior angle: \(f^\circ\).
- Another interior angle: \(90^\circ\) (right angle).
- Exterior angle: \(153^\circ\).

Using the Exterior Angle Theorem:
\[
153^\circ = f^\circ + 90^\circ
\]
Solving for \(f\):
\[
f = 153^\circ - 90^\circ = 63^\circ
\]

Answer:
\[
\boxed{63}
\]

---

Problem 8:


Given:
- Two interior angles: \(31^\circ\) and \(31^\circ\).
- Exterior angle: \(s^\circ\).

Using the Exterior Angle Theorem:
\[
s = 31^\circ + 31^\circ = 62^\circ
\]

Answer:
\[
\boxed{62}
\]

---

Final Answers:

\[
\boxed{116, 114, 57, 146, 53, 52, 63, 62}
\]