Finding Measures of Vertical Angles in Geometry

The video tutorial explains the concept of intersecting lines and vertical angles. It introduces two intersecting lines with angles expressed as algebraic expressions. The tutorial demonstrates how to solve for x by equating the expressions of vertical angles, which are equal. After finding x, the video shows how to calculate the actual angle measures, confirming they are equal. The tutorial emphasizes understanding vertical angles and solving algebraic equations to find angle measures.

What is the measure of the first angle given in the problem?

• 9x + 182 degrees

• 7x + 182 degrees

• 9x + 194 degrees

• 7x + 194 degrees

What is the measure of the second angle given in the problem?

• 7x + 194 degrees

• 9x + 194 degrees

• 7x + 182 degrees

• 9x + 182 degrees

What type of angles are the two given angles?

• Complementary angles

• Vertical angles

• Supplementary angles

• Adjacent angles

What equation can be set up based on the fact that the angles are vertical angles?

• 7x - 182 = 9x + 194

• 7x - 182 = 9x - 194

• 7x + 182 = 9x - 194

• 7x + 182 = 9x + 194

What is the first step in solving the equation 9x + 194 = 7x + 182?

• Add 7x to both sides

• Subtract 7x from both sides

• Subtract 194 from both sides

• Add 194 to both sides

After simplifying the equation, what is the resulting equation before solving for x?

• x = -12

• x = 12

• 2x = -12

• 2x = 12

What is the value of x after solving the equation?

• x = -12

• x = 12

• x = -6

• x = 6

What is the measure of the angle calculated using 7x + 182 when x = -6?

• 170 degrees

• 160 degrees

• 150 degrees

• 140 degrees

What is the measure of the angle calculated using 9x + 194 when x = -6?

• 140 degrees

• 170 degrees

• 150 degrees

• 160 degrees

What is the final measure of both angles?

• 160 degrees

• 150 degrees

• 140 degrees

• 130 degrees