Angle Sum Property and Exterior Angle Theorem | Triangle Worksheets - Free Printable

To solve the problem of finding the measures of the indicated angles in each triangle, we will use the Triangle Angle Sum Theorem, which states that the sum of the interior angles of a triangle is always 180°. Additionally, we may use properties of specific types of triangles (e.g., right triangles, isosceles triangles) and supplementary angles if needed.

Let's go through each problem step by step:

---

Problem 1:

[Image shows a triangle with one angle labeled as \( m\angle A \), and the other two angles are given as 50° and 60°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle A + 50^\circ + 60^\circ = 180^\circ
\]
Simplify:
\[
m\angle A + 110^\circ = 180^\circ
\]
Solve for \( m\angle A \):
\[
m\angle A = 180^\circ - 110^\circ = 70^\circ
\]

#### Answer:
\[
\boxed{70^\circ}
\]

---

Problem 2:

[Image shows a right triangle with one angle labeled as \( m\angle B \), and the other non-right angle is given as 35°.]

#### Solution:
In a right triangle, one angle is always 90°. The sum of the interior angles is 180°. Therefore:
\[
m\angle B + 35^\circ + 90^\circ = 180^\circ
\]
Simplify:
\[
m\angle B + 125^\circ = 180^\circ
\]
Solve for \( m\angle B \):
\[
m\angle B = 180^\circ - 125^\circ = 55^\circ
\]

#### Answer:
\[
\boxed{55^\circ}
\]

---

Problem 3:

[Image shows an isosceles triangle with one angle labeled as \( m\angle C \), and the base angles are given as 40° each.]

#### Solution:
In an isosceles triangle, the base angles are equal. The sum of the interior angles is 180°. Therefore:
\[
m\angle C + 40^\circ + 40^\circ = 180^\circ
\]
Simplify:
\[
m\angle C + 80^\circ = 180^\circ
\]
Solve for \( m\angle C \):
\[
m\angle C = 180^\circ - 80^\circ = 100^\circ
\]

#### Answer:
\[
\boxed{100^\circ}
\]

---

Problem 4:

[Image shows a triangle with one angle labeled as \( m\angle D \), and the other two angles are given as 70° and 50°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle D + 70^\circ + 50^\circ = 180^\circ
\]
Simplify:
\[
m\angle D + 120^\circ = 180^\circ
\]
Solve for \( m\angle D \):
\[
m\angle D = 180^\circ - 120^\circ = 60^\circ
\]

#### Answer:
\[
\boxed{60^\circ}
\]

---

Problem 5:

[Image shows a triangle with one angle labeled as \( m\angle E \), and the other two angles are given as 30° and 60°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle E + 30^\circ + 60^\circ = 180^\circ
\]
Simplify:
\[
m\angle E + 90^\circ = 180^\circ
\]
Solve for \( m\angle E \):
\[
m\angle E = 180^\circ - 90^\circ = 90^\circ
\]

#### Answer:
\[
\boxed{90^\circ}
\]

---

Problem 6:

[Image shows a triangle with one angle labeled as \( m\angle F \), and the other two angles are given as 45° and 45°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle F + 45^\circ + 45^\circ = 180^\circ
\]
Simplify:
\[
m\angle F + 90^\circ = 180^\circ
\]
Solve for \( m\angle F \):
\[
m\angle F = 180^\circ - 90^\circ = 90^\circ
\]

#### Answer:
\[
\boxed{90^\circ}
\]

---

Problem 7:

[Image shows a triangle with one angle labeled as \( m\angle G \), and the other two angles are given as 20° and 70°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle G + 20^\circ + 70^\circ = 180^\circ
\]
Simplify:
\[
m\angle G + 90^\circ = 180^\circ
\]
Solve for \( m\angle G \):
\[
m\angle G = 180^\circ - 90^\circ = 90^\circ
\]

#### Answer:
\[
\boxed{90^\circ}
\]

---

Problem 8:

[Image shows a triangle with one angle labeled as \( m\angle H \), and the other two angles are given as 30° and 80°.]

#### Solution:
The sum of the interior angles of a triangle is 180°. Therefore:
\[
m\angle H + 30^\circ + 80^\circ = 180^\circ
\]
Simplify:
\[
m\angle H + 110^\circ = 180^\circ
\]
Solve for \( m\angle H \):
\[
m\angle H = 180^\circ - 110^\circ = 70^\circ
\]

#### Answer:
\[
\boxed{70^\circ}
\]

---

Final Answers:

\[
\boxed{70^\circ, 55^\circ, 100^\circ, 60^\circ, 90^\circ, 90^\circ, 90^\circ, 70^\circ}
\]