Triangle Angles and Relationships

The video tutorial explains how to solve a triangle problem using three equations with three unknowns. It begins by defining the problem and setting up equations based on given constraints. The tutorial then demonstrates how to eliminate variables and solve the system of equations to find the measures of the three angles. Finally, it verifies the solution by checking the constraints and concludes the problem.

What is the sum of the angles in a triangle?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

If the second angle is 50 degrees less than four times the first angle, how can it be expressed in terms of the first angle?

• 4a + 50

• a + 50

• a - 50

• 4a - 50

How is the third angle related to the first angle?

• It is twice the first angle.

• It is equal to the first angle.

• It is 40 degrees less than the first angle.

• It is 40 degrees more than the first angle.

What is the first step in solving the system of equations for the triangle angles?

• Multiply all equations by a constant.

• Rearrange the equations to isolate variables.

• Subtract the first equation from the second.

• Add all equations together.

What is the value of the first angle, a, after solving the equations?

• 90 degrees

• 60 degrees

• 45 degrees

• 30 degrees

How do you find the value of the third angle, c, once you know the first angle?

• Subtract 40 from the first angle.

• Divide the first angle by 2.

• Add 40 to the first angle.

• Multiply the first angle by 2.

What is the measure of the third angle, c?

• 10 degrees

• 5 degrees

• 20 degrees

• 15 degrees

How is the second angle, b, calculated once the first angle is known?

• b = a - 50

• b = 4a + 50

• b = 4a - 50

• b = a + 50

What is the measure of the second angle, b?

• 100 degrees

• 110 degrees

• 120 degrees

• 130 degrees

Which of the following verifies that the solution meets all constraints?

• The third angle is 40 degrees less than the first angle.

• The second angle is 50 degrees more than four times the first angle.

• The sum of angles is 200 degrees.

• The first angle is 50 degrees.