Triangles Find Missing Angle worksheet - Free Printable

To solve the problems, we need to use the properties of triangles, specifically the fact that the sum of the interior angles of a triangle is always 180°. Additionally, we will use the properties of isosceles and right triangles where applicable.

Let's solve each problem step by step:

---

Problem 1:

- Triangle ABC is a right triangle (one angle is 90°).
- Given: ∠B = 22°, ∠A = 90°.
- To find: ∠C = x.

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
\angle A + \angle B + \angle C = 180^\circ
\]
\[
90^\circ + 22^\circ + x = 180^\circ
\]
\[
112^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 112^\circ
\]
\[
x = 68^\circ
\]

Answer: \( x = 68^\circ \)

---

Problem 2:

- Triangle ABC is an isosceles triangle (two sides are equal, so two angles are equal).
- Given: The two base angles are marked as \( x \).
- To find: \( x \).

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + x + 90^\circ = 180^\circ
\]
\[
2x + 90^\circ = 180^\circ
\]
\[
2x = 180^\circ - 90^\circ
\]
\[
2x = 90^\circ
\]
\[
x = \frac{90^\circ}{2}
\]
\[
x = 45^\circ
\]

Answer: \( x = 45^\circ \)

---

Problem 3:

- Triangle ABC is an isosceles triangle (two sides are equal, so two angles are equal).
- Given: One base angle is 55°.
- To find: The vertex angle \( x \).

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 55^\circ + 55^\circ = 180^\circ
\]
\[
x + 110^\circ = 180^\circ
\]
\[
x = 180^\circ - 110^\circ
\]
\[
x = 70^\circ
\]

Answer: \( x = 70^\circ \)

---

Problem 4:

- Triangle ABC is an isosceles triangle (two sides are equal, so two angles are equal).
- Given: One base angle is 68° and the vertex angle is 52°.
- To find: The other base angle \( x \).

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 68^\circ + 52^\circ = 180^\circ
\]
\[
x + 120^\circ = 180^\circ
\]
\[
x = 180^\circ - 120^\circ
\]
\[
x = 60^\circ
\]

Answer: \( x = 60^\circ \)

---

Problem 5:

- Triangle ABC is a right triangle (one angle is 90°).
- Given: ∠B = 43°.
- To find: ∠A = x.

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 43^\circ + 90^\circ = 180^\circ
\]
\[
x + 133^\circ = 180^\circ
\]
\[
x = 180^\circ - 133^\circ
\]
\[
x = 47^\circ
\]

Answer: \( x = 47^\circ \)

---

Problem 6:

- Triangle ABC is an isosceles triangle (two sides are equal, so two angles are equal).
- Given: One base angle is 52° and the vertex angle is 74°.
- To find: The other base angle \( x \).

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 52^\circ + 74^\circ = 180^\circ
\]
\[
x + 126^\circ = 180^\circ
\]
\[
x = 180^\circ - 126^\circ
\]
\[
x = 54^\circ
\]

Answer: \( x = 54^\circ \)

---

Problem 7:

- Triangle ABC is a scalene triangle.
- Given: ∠A = 82° and ∠B = 22°.
- To find: ∠C = x.

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 82^\circ + 22^\circ = 180^\circ
\]
\[
x + 104^\circ = 180^\circ
\]
\[
x = 180^\circ - 104^\circ
\]
\[
x = 76^\circ
\]

Answer: \( x = 76^\circ \)

---

Problem 8:

- Triangle ABC is a right triangle (one angle is 90°).
- Given: ∠A = 64°.
- To find: ∠B = x.

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 64^\circ + 90^\circ = 180^\circ
\]
\[
x + 154^\circ = 180^\circ
\]
\[
x = 180^\circ - 154^\circ
\]
\[
x = 26^\circ
\]

Answer: \( x = 26^\circ \)

---

Problem 9:

- Triangle ABC is a scalene triangle.
- Given: ∠B = 54° and ∠A = 49°.
- To find: ∠C = x.

Using the triangle angle sum property:
\[
\text{Sum of angles in a triangle} = 180^\circ
\]
\[
x + 54^\circ + 49^\circ = 180^\circ
\]
\[
x + 103^\circ = 180^\circ
\]
\[
x = 180^\circ - 103^\circ
\]
\[
x = 77^\circ
\]

Answer: \( x = 77^\circ \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 68^\circ \\
2. & 45^\circ \\
3. & 70^\circ \\
4. & 60^\circ \\
5. & 47^\circ \\
6. & 54^\circ \\
7. & 76^\circ \\
8. & 26^\circ \\
9. & 77^\circ \\
\end{array}
}
\]