Missing Angles worksheet - Free Printable

Problem Analysis

The task involves determining the missing angles in each of the given diagrams. The key principle to use here is that angles on a straight line add up to 180°. This means that if two angles are adjacent and form a straight line, their sum must be 180°.

Step-by-Step Solution

#### 1)
- Given: One angle is \(47^\circ\).
- Missing angle: \(a^\circ\).
- Since the two angles are on a straight line:
\[
47^\circ + a^\circ = 180^\circ
\]
Solving for \(a\):
\[
a = 180^\circ - 47^\circ = 133^\circ
\]

#### 2)
- Given: One angle is \(118^\circ\).
- Missing angle: \(x^\circ\).
- Since the two angles are on a straight line:
\[
118^\circ + x^\circ = 180^\circ
\]
Solving for \(x\):
\[
x = 180^\circ - 118^\circ = 62^\circ
\]

#### 3)
- Given: Two equal angles labeled as \(n^\circ\) on a straight line.
- Since the two angles are equal and on a straight line:
\[
n^\circ + n^\circ = 180^\circ
\]
Simplifying:
\[
2n = 180^\circ
\]
Solving for \(n\):
\[
n = \frac{180^\circ}{2} = 90^\circ
\]

#### 4)
- Given: One angle is \(134^\circ\).
- Missing angle: \(y^\circ\).
- Since the two angles are on a straight line:
\[
y^\circ + 134^\circ = 180^\circ
\]
Solving for \(y\):
\[
y = 180^\circ - 134^\circ = 46^\circ
\]

#### 5)
- Given: One angle is \(153^\circ\).
- Missing angle: \(b^\circ\).
- Since the two angles are on a straight line:
\[
b^\circ + 153^\circ = 180^\circ
\]
Solving for \(b\):
\[
b = 180^\circ - 153^\circ = 27^\circ
\]

#### 6)
- Given: One angle is \(165^\circ\).
- Missing angle: \(g^\circ\).
- Since the two angles are on a straight line:
\[
g^\circ + 165^\circ = 180^\circ
\]
Solving for \(g\):
\[
g = 180^\circ - 165^\circ = 15^\circ
\]

Final Answers

\[
\boxed{
\begin{aligned}
1) & \quad a = 133^\circ \\
2) & \quad x = 62^\circ \\
3) & \quad n = 90^\circ \\
4) & \quad y = 46^\circ \\
5) & \quad b = 27^\circ \\
6) & \quad g = 15^\circ
\end{aligned}
}
\]