Questions: English ~ Brayden Bentley Using Vertical Angles to Find Unknown Values

To find unknown values using vertical angles, we need to understand the concept of vertical angles. Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Here's a step-by-step guide on how to use vertical angles to find unknown values:

1. Identify the Vertical Angles: When two lines intersect, they form two pairs of vertical angles. For example, if two lines intersect and form angles A, B, C, and D, then angle A is vertical to angle C, and angle B is vertical to angle D.

2. Set the Angles Equal: Since vertical angles are equal, you can set the measures of the vertical angles equal to each other. For example, if angle A is vertical to angle C, then the measure of angle A is equal to the measure of angle C.

3. Solve for the Unknown: If one of the angles is unknown, you can use the equation from step 2 to solve for the unknown value. For example, if angle A is 50 degrees and angle C is unknown, you can set up the equation: \[ A = C \implies 50 = C \] Therefore, angle C is also 50 degrees.

4. Check Your Work: After finding the unknown value, it's always a good idea to check your work by ensuring that all pairs of vertical angles are equal.

Example Problem: Suppose two lines intersect, forming angles of 3x + 10 degrees and 5x - 20 degrees. Find the value of x.

Solution:

• Since the angles are vertical, they are equal: \[ 3x + 10 = 5x - 20 \]
• Solve for x: \[ 3x + 10 = 5x - 20 \\ 10 + 20 = 5x - 3x \\ 30 = 2x \\ x = 15 \]

Therefore, the value of x is 15.