Finding missing angles worksheet - Free Printable

Problem: Solve the missing angles in the given diagrams and explain the solution.

#### Step 1: Name the angles (Part 1)
We are asked to name the angles based on their types. Let's identify each angle:

- A: This is a reflex angle (greater than 180° but less than 360°).
- B: This is a right angle (exactly 90°).
- C: This is an acute angle (less than 90°).
- D: This is an obtuse angle (greater than 90° but less than 180°).

So, the answers are:
- A: Reflex angle
- B: Right angle
- C: Acute angle
- D: Obtuse angle

---

#### Step 2: Find the missing angles (Part 2)

We will solve each part step by step using the properties of angles:
1. Angles on a straight line add up to 180°.
2. Angles around a point add up to 360°.
3. In a right triangle, the sum of the angles is 180°.
4. Vertically opposite angles are equal.
5. Corresponding or alternate angles are equal when lines are parallel.

##### (a)
The diagram shows two angles on a straight line: one is 22°, and the other is labeled as \( a \).

Using the property that angles on a straight line add up to 180°:
\[
a + 22^\circ = 180^\circ
\]
\[
a = 180^\circ - 22^\circ = 158^\circ
\]

So, \( a = 158^\circ \).

##### (b)
The diagram shows a right triangle with one angle of 38° and another angle labeled as \( b \). The third angle is a right angle (90°).

Using the property that the sum of angles in a triangle is 180°:
\[
b + 38^\circ + 90^\circ = 180^\circ
\]
\[
b + 128^\circ = 180^\circ
\]
\[
b = 180^\circ - 128^\circ = 52^\circ
\]

So, \( b = 52^\circ \).

##### (c)
The diagram shows two intersecting lines with one angle labeled as 51° and another angle labeled as \( c \). The angles are vertically opposite.

Using the property that vertically opposite angles are equal:
\[
c = 51^\circ
\]

So, \( c = 51^\circ \).

##### (d)
The diagram shows two angles on a straight line: one is 65°, and the other is labeled as \( d \).

Using the property that angles on a straight line add up to 180°:
\[
d + 65^\circ = 180^\circ
\]
\[
d = 180^\circ - 65^\circ = 115^\circ
\]

So, \( d = 115^\circ \).

##### (e)
The diagram shows two intersecting lines with one angle labeled as 130° and another angle labeled as \( e \). The angles are supplementary (on a straight line).

Using the property that angles on a straight line add up to 180°:
\[
e + 130^\circ = 180^\circ
\]
\[
e = 180^\circ - 130^\circ = 50^\circ
\]

So, \( e = 50^\circ \).

##### (f)
The diagram shows two intersecting lines with one angle labeled as 145° and another angle labeled as \( g \). The angles are vertically opposite.

Using the property that vertically opposite angles are equal:
\[
g = 145^\circ
\]

So, \( g = 145^\circ \).

##### (g)
The diagram shows a triangle with two angles labeled as 73° and 38°, and the third angle is labeled as \( h \).

Using the property that the sum of angles in a triangle is 180°:
\[
h + 73^\circ + 38^\circ = 180^\circ
\]
\[
h + 111^\circ = 180^\circ
\]
\[
h = 180^\circ - 111^\circ = 69^\circ
\]

So, \( h = 69^\circ \).

##### (h)
The diagram shows two intersecting lines with one angle labeled as 85° and another angle labeled as \( i \). The angles are vertically opposite.

Using the property that vertically opposite angles are equal:
\[
i = 85^\circ
\]

So, \( i = 85^\circ \).

##### (i)
The diagram shows two intersecting lines with one angle labeled as 73° and another angle labeled as \( j \). The angles are supplementary (on a straight line).

Using the property that angles on a straight line add up to 180°:
\[
j + 73^\circ = 180^\circ
\]
\[
j = 180^\circ - 73^\circ = 107^\circ
\]

So, \( j = 107^\circ \).

---

Final Answers:

\[
\boxed{
\begin{aligned}
&\text{(a)} \, a = 158^\circ \\
&\text{(b)} \, b = 52^\circ \\
&\text{(c)} \, c = 51^\circ \\
&\text{(d)} \, d = 115^\circ \\
&\text{(e)} \, e = 50^\circ \\
&\text{(f)} \, g = 145^\circ \\
&\text{(g)} \, h = 69^\circ \\
&\text{(h)} \, i = 85^\circ \\
&\text{(i)} \, j = 107^\circ
\end{aligned}
}
\]