Vertical Angles Worksheets - Free Printable

To find the measure of angle $x$ in each figure, we need to use the properties of vertical angles and straight lines.

Key Rules:
1. Vertical Angles: Angles opposite each other where two lines cross are equal.
2. Straight Line: Angles on a straight line add up to $180^\circ$.
3. Right Angle: A square symbol means the angle is $90^\circ$.

Here is the step-by-step solution for each problem:

1)
* The angle labeled $45^\circ$ and angle $y$ are vertical angles, so $y = 45^\circ$.
* Angles $x$, $y$, and the right angle ($90^\circ$) form a straight line.
* Equation: $x + y + 90^\circ = 180^\circ$
* Substitute $y$: $x + 45^\circ + 90^\circ = 180^\circ$
* $x + 135^\circ = 180^\circ$
* $x = 180^\circ - 135^\circ$
* $x = 45^\circ$

2)
* Angle $y$ and the angle labeled $35^\circ$ are vertical angles, so $y = 35^\circ$.
* Angle $x$ and the $35^\circ$ angle form a right angle ($90^\circ$).
* Equation: $x + 35^\circ = 90^\circ$
* $x = 90^\circ - 35^\circ$
* $x = 55^\circ$

3)
* Angle $y$ and the angle labeled $60^\circ$ are vertical angles, so $y = 60^\circ$.
* Angles $x$, $y$, and $70^\circ$ form a straight line ($180^\circ$).
* Equation: $x + y + 70^\circ = 180^\circ$
* Substitute $y$: $x + 60^\circ + 70^\circ = 180^\circ$
* $x + 130^\circ = 180^\circ$
* $x = 180^\circ - 130^\circ$
* $x = 50^\circ$

4)
* Angle $x$ and the angle labeled $40^\circ$ are vertical angles.
* Therefore, they are equal.
* $x = 40^\circ$

5)
* There is a right angle symbol ($90^\circ$) between the vertical line and the horizontal line on the left.
* Angle $x$ and the angle labeled $35^\circ$ make up that $90^\circ$ angle.
* Equation: $x + 35^\circ = 90^\circ$
* $x = 90^\circ - 35^\circ$
* $x = 55^\circ$

6)
* Angle $x$ and the angle labeled $25^\circ$ form a straight line ($180^\circ$).
* Equation: $x + 25^\circ = 180^\circ$
* $x = 180^\circ - 25^\circ$
* $x = 155^\circ$

Final Answer:
1) x = 45°
2) x = 55°
3) x = 50°
4) x = 40°
5) x = 55°
6) x = 155°