Angles Worksheet 10 with Clues - Practice finding missing angles using geometric properties and reasoning.

To solve the problems in the "Angles Worksheet 10," we need to use various angle properties and relationships. Below, I will explain how to solve each section step by step.

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Section A: State the missing angle and give a reason for your answer

#### 1)
- Given: One angle is \(48^\circ\).
- The two angles form a straight line.
- Reason: Angles on a straight line sum to \(180^\circ\).
- Calculation: \(180^\circ - 48^\circ = 132^\circ\).
- Answer: Angle \(x = 132^\circ\).

#### 2)
- Given: One angle is \(52^\circ\).
- The two angles are adjacent and form a right angle (90°).
- Reason: Angles forming a right angle sum to \(90^\circ\).
- Calculation: \(90^\circ - 52^\circ = 38^\circ\).
- Answer: Angle \(x = 38^\circ\).

#### 3)
- Given: One angle is \(65^\circ\).
- The two angles are vertical angles.
- Reason: Vertical angles are equal.
- Calculation: \(x = 65^\circ\).
- Answer: Angle \(x = 65^\circ\).

#### 4)
- Given: One angle is \(71^\circ\).
- The two angles are alternate interior angles.
- Reason: Alternate interior angles are equal when lines are parallel.
- Calculation: \(x = 71^\circ\).
- Answer: Angle \(x = 71^\circ\).

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Section B: Calculate the missing angle and give a reason for your answer

#### 1)
- Given: One angle is \(108^\circ\).
- The two angles are supplementary (form a straight line).
- Reason: Angles on a straight line sum to \(180^\circ\).
- Calculation: \(180^\circ - 108^\circ = 72^\circ\).
- Answer: Angle \(a = 72^\circ\).

#### 2)
- Given: One angle is \(43^\circ\).
- The two angles are corresponding angles.
- Reason: Corresponding angles are equal when lines are parallel.
- Calculation: \(b = 43^\circ\).
- Answer: Angle \(b = 43^\circ\).

#### 3)
- Given: One angle is \(114^\circ\).
- The two angles are alternate exterior angles.
- Reason: Alternate exterior angles are equal when lines are parallel.
- Calculation: \(c = 114^\circ\).
- Answer: Angle \(c = 114^\circ\).

#### 4)
- Given: One angle is \(79^\circ\).
- The two angles are co-interior angles (also called consecutive interior angles).
- Reason: Co-interior angles sum to \(180^\circ\) when lines are parallel.
- Calculation: \(180^\circ - 79^\circ = 101^\circ\).
- Answer: Angle \(d = 101^\circ\).

#### 5)
- Given: One angle is \(82^\circ\).
- The two angles are vertically opposite angles.
- Reason: Vertically opposite angles are equal.
- Calculation: \(e = 82^\circ\).
- Answer: Angle \(e = 82^\circ\).

#### 6)
- Given: One angle is \(67^\circ\).
- The two angles are alternate interior angles.
- Reason: Alternate interior angles are equal when lines are parallel.
- Calculation: \(f = 67^\circ\).
- Answer: Angle \(f = 67^\circ\).

#### 7)
- Given: One angle is \(127^\circ\).
- The two angles are supplementary (form a straight line).
- Reason: Angles on a straight line sum to \(180^\circ\).
- Calculation: \(180^\circ - 127^\circ = 53^\circ\).
- Answer: Angle \(g = 53^\circ\).

#### 8)
- Given: One angle is \(24^\circ\).
- The two angles are corresponding angles.
- Reason: Corresponding angles are equal when lines are parallel.
- Calculation: \(k = 24^\circ\).
- Answer: Angle \(k = 24^\circ\).

#### 9)
- Given: One angle is \(77^\circ\).
- The two angles are alternate interior angles.
- Reason: Alternate interior angles are equal when lines are parallel.
- Calculation: \(m = 77^\circ\).
- Answer: Angle \(m = 77^\circ\).

#### 10)
- Given: One angle is \(94^\circ\).
- The two angles are co-interior angles.
- Reason: Co-interior angles sum to \(180^\circ\) when lines are parallel.
- Calculation: \(180^\circ - 94^\circ = 86^\circ\).
- Answer: Angle \(n = 86^\circ\).

#### 11)
- Given: One angle is \(155^\circ\).
- The two angles are supplementary (form a straight line).
- Reason: Angles on a straight line sum to \(180^\circ\).
- Calculation: \(180^\circ - 155^\circ = 25^\circ\).
- Answer: Angle \(p = 25^\circ\).

#### 12)
- Given: One angle is \(119^\circ\).
- The two angles are alternate exterior angles.
- Reason: Alternate exterior angles are equal when lines are parallel.
- Calculation: \(q = 119^\circ\).
- Answer: Angle \(q = 119^\circ\).

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Final Answers

\[
\boxed{
\begin{array}{ll}
\text{Section A:} & \text{1) } x = 132^\circ, \text{2) } x = 38^\circ, \text{3) } x = 65^\circ, \text{4) } x = 71^\circ \\
\text{Section B:} & \text{1) } a = 72^\circ, \text{2) } b = 43^\circ, \text{3) } c = 114^\circ, \text{4) } d = 101^\circ, \\
& \text{5) } e = 82^\circ, \text{6) } f = 67^\circ, \text{7) } g = 53^\circ, \text{8) } k = 24^\circ, \\
& \text{9) } m = 77^\circ, \text{10) } n = 86^\circ, \text{11) } p = 25^\circ, \text{12) } q = 119^\circ
\end{array}
}
\]