Finding missing angles worksheet - Free Printable

Problem Overview:

The task involves finding the missing angles in various geometric shapes, primarily triangles and quadrilaterals. The key principles to use are:
1. Angles in a triangle add up to 180°.
2. Angles in a quadrilateral add up to 360°.
3. Opposite angles in certain shapes (like parallelograms) are equal.

Let's solve each part step by step.

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Section 3: Triangles

#### a)
- Given angles: 65° and 55°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (65° + 55°) = 180° - 120° = 60° \).

Answer: 60°

#### b)
- Given angles: 43° and 83°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (43° + 83°) = 180° - 126° = 54° \).

Answer: 54°

#### c)
- Given angles: 48° and 48°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (48° + 48°) = 180° - 96° = 84° \).

Answer: 84°

#### d)
- Given angles: 50° and 90° (right angle).
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (50° + 90°) = 180° - 140° = 40° \).

Answer: 40°

#### e)
- Given angles: 38° and 132°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (38° + 132°) = 180° - 170° = 10° \).

Answer: 10°

#### f)
- Given angles: 11° and 78°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (11° + 78°) = 180° - 89° = 91° \).

Answer: 91°

#### g)
- Given angles: 50° and 70°.
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (50° + 70°) = 180° - 120° = 60° \).

Answer: 60°

#### h)
- Given angles: 45° and 90° (right angle).
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (45° + 90°) = 180° - 135° = 45° \).

Answer: 45°

#### i)
- Given angles: 75° and 90° (right angle).
- Sum of angles in a triangle = 180°.
- Missing angle = \( 180° - (75° + 90°) = 180° - 165° = 15° \).

Answer: 15°

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Section 4: Quadrilaterals

#### a)
- Given angles: 130°, 75°, and 85°.
- Sum of angles in a quadrilateral = 360°.
- Missing angle \( a \) = \( 360° - (130° + 75° + 85°) = 360° - 290° = 70° \).

Answer: 70°

#### b)
- Given angles: 126°, 59°, and 64°.
- Sum of angles in a quadrilateral = 360°.
- Missing angle \( b \) = \( 360° - (126° + 59° + 64°) = 360° - 249° = 111° \).

Answer: 111°

#### c)
- Given angles: 154°, 58°, and 90° (right angle).
- Sum of angles in a quadrilateral = 360°.
- Missing angle \( c \) = \( 360° - (154° + 58° + 90°) = 360° - 302° = 58° \).

Answer: 58°

#### d)
- Given angles: 97°, 52°, and 90° (right angle).
- Sum of angles in a quadrilateral = 360°.
- Missing angle \( h \) = \( 360° - (97° + 52° + 90°) = 360° - 239° = 121° \).

Answer: 121°

#### e)
- Given angles: 123°, 51°, and 85°.
- Sum of angles in a quadrilateral = 360°.
- Missing angle \( k \) = \( 360° - (123° + 51° + 85°) = 360° - 259° = 101° \).

Answer: 101°

#### f)
- This is a pair of intersecting lines forming vertical angles.
- Vertical angles are equal.
- Given angles: 131°, 103°, and 83°.
- Missing angle \( m \):
- Opposite angle to 131° is \( m \), so \( m = 131° \).
- Missing angle \( n \):
- Opposite angle to 83° is \( n \), so \( n = 83° \).

Answer: \( m = 131° \), \( n = 83° \)

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Final Answers:

Section 3:
a) 60°
b) 54°
c) 84°
d) 40°
e) 10°
f) 91°
g) 60°
h) 45°
i) 15°

Section 4:
a) 70°
b) 111°
c) 58°
d) 121°
e) 101°
f) \( m = 131° \), \( n = 83° \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Section 3:} \\
\text{a) } 60°, \text{b) } 54°, \text{c) } 84°, \text{d) } 40°, \text{e) } 10°, \text{f) } 91°, \text{g) } 60°, \text{h) } 45°, \text{i) } 15° \\
\text{Section 4:} \\
\text{a) } 70°, \text{b) } 111°, \text{c) } 58°, \text{d) } 121°, \text{e) } 101°, \text{f) } m = 131°, n = 83°
\end{array}
}
\]