Solving Linear Equations and Angles

The video tutorial explains how to solve problems involving vertical angles. It begins by introducing vertical angles and setting up an equation to find the value of x. The instructor solves the first equation, 62 = 11x + 7, to find x = 5. Next, the instructor labels angles QRS and TRV and sets up a second equation, 5x + 10 = 10x - 50. By solving this equation, the instructor finds x = 12. Finally, the instructor calculates the measure of the angle using the value of x, resulting in a measure of 70°.

What is a key property of vertical angles?

• They are always right angles.

• They are equal in measure.

• They are always supplementary.

• They are always complementary.

If two vertical angles are given as 62° and 11x + 7, what equation can be set up?

• 62 * 11x = 7

• 62 - 11x = 7

• 62 = 11x + 7

• 62 + 11x = 7

What is the first step in solving the equation 62 = 11x + 7?

• Add 7 to both sides.

• Divide both sides by 11.

• Subtract 7 from both sides.

• Multiply both sides by 11.

After subtracting 7 from both sides in the equation 62 = 11x + 7, what is the next step?

• Add 11 to both sides.

• Subtract 11 from both sides.

• Divide both sides by 11.

• Multiply both sides by 11.

What is the value of x when solving the equation 55 = 11x?

• x = 5

• x = 6

• x = 7

• x = 8

What is the relationship between angles QRS and TRV?

• They are supplementary.

• They are vertical angles.

• They are complementary.

• They are adjacent angles.

How do you set up an equation for angles represented by 5x + 10 and 10x - 50?

• 5x + 10 - 10x = 50

• 5x + 10 = 10x - 50

• 5x + 10 + 10x = 50

• 5x + 10 * 10x = 50

What is the first step in solving the equation 5x + 10 = 10x - 50?

• Multiply both sides by 5.

• Subtract 5x from both sides.

• Add 5x to both sides.

• Divide both sides by 5.

After subtracting 5x from both sides in the equation 5x + 10 = 10x - 50, what is the next step?

• Add 50 to both sides.

• Divide both sides by 5.

• Multiply both sides by 5.

• Subtract 50 from both sides.

What is the value of x when solving the equation 60 = 5x?

• x = 10

• x = 11

• x = 12

• x = 13