Worksheet for finding missing angles in geometric figures.

To solve the missing angles in the given worksheet, we need to use basic geometric principles such as:

1. Sum of angles around a point: The sum of all angles around a point is \(360^\circ\).
2. Sum of angles on a straight line: The sum of angles on a straight line is \(180^\circ\).
3. Sum of angles in a triangle: The sum of the interior angles in a triangle is \(180^\circ\).
4. Right angle: A right angle measures \(90^\circ\).

Let's solve each problem step by step.

---

Problem 1:


- The diagram shows a right angle (\(90^\circ\)) and another angle (\(20^\circ\)).
- The missing angle \(x\) can be found using the fact that the sum of angles on a straight line is \(180^\circ\):
\[
x + 90^\circ + 20^\circ = 180^\circ
\]
\[
x + 110^\circ = 180^\circ
\]
\[
x = 70^\circ
\]

Answer for Problem 1: \(x = 70^\circ\)

---

Problem 2:


- The diagram shows an angle of \(140^\circ\) and a missing angle \(x\).
- These two angles are on a straight line, so their sum is \(180^\circ\):
\[
x + 140^\circ = 180^\circ
\]
\[
x = 40^\circ
\]

Answer for Problem 2: \(x = 40^\circ\)

---

Problem 3:


- The diagram shows a right triangle with angles \(30^\circ\) and \(60^\circ\).
- The sum of the angles in a triangle is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 30^\circ + 60^\circ = 180^\circ
\]
\[
x + 90^\circ = 180^\circ
\]
\[
x = 90^\circ
\]

Answer for Problem 3: \(x = 90^\circ\)

---

Problem 4:


- The diagram shows a right angle (\(90^\circ\)) and two other angles (\(15^\circ\) and \(10^\circ\)).
- The missing angle \(x\) can be found using the fact that the sum of angles around a point is \(360^\circ\):
\[
x + 90^\circ + 15^\circ + 10^\circ = 360^\circ
\]
\[
x + 115^\circ = 360^\circ
\]
\[
x = 245^\circ
\]

Answer for Problem 4: \(x = 245^\circ\)

---

Problem 5:


- The diagram shows a right triangle with one angle \(25^\circ\) and another angle \(x\).
- The sum of the angles in a triangle is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 25^\circ + 90^\circ = 180^\circ
\]
\[
x + 115^\circ = 180^\circ
\]
\[
x = 65^\circ
\]

Answer for Problem 5: \(x = 65^\circ\)

---

Problem 6:


- The diagram shows a triangle with angles \(45^\circ\), \(60^\circ\), and a missing angle \(x\).
- The sum of the angles in a triangle is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 45^\circ + 60^\circ = 180^\circ
\]
\[
x + 105^\circ = 180^\circ
\]
\[
x = 75^\circ
\]

Answer for Problem 6: \(x = 75^\circ\)

---

Problem 7:


- The diagram shows a triangle with angles \(40^\circ\) and \(3x\), and a missing angle \(x\).
- The sum of the angles in a triangle is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 40^\circ + 3x = 180^\circ
\]
\[
4x + 40^\circ = 180^\circ
\]
\[
4x = 140^\circ
\]
\[
x = 35^\circ
\]

Answer for Problem 7: \(x = 35^\circ\)

---

Problem 8:


- The diagram shows three angles on a straight line: \(10^\circ\), \(x\), and \(20^\circ\).
- The sum of angles on a straight line is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 10^\circ + 20^\circ = 180^\circ
\]
\[
x + 30^\circ = 180^\circ
\]
\[
x = 150^\circ
\]

Answer for Problem 8: \(x = 150^\circ\)

---

Problem 9:


- The diagram shows a triangle with angles \(50^\circ\), \(50^\circ\), and a missing angle \(x\).
- The sum of the angles in a triangle is \(180^\circ\). The missing angle \(x\) can be found as:
\[
x + 50^\circ + 50^\circ = 180^\circ
\]
\[
x + 100^\circ = 180^\circ
\]
\[
x = 80^\circ
\]

Answer for Problem 9: \(x = 80^\circ\)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & x = 70^\circ \\
2) & x = 40^\circ \\
3) & x = 90^\circ \\
4) & x = 245^\circ \\
5) & x = 65^\circ \\
6) & x = 75^\circ \\
7) & x = 35^\circ \\
8) & x = 150^\circ \\
9) & x = 80^\circ \\
\end{array}
}
\]