Triangle Angle Relationships and Measures

This video tutorial explains how to find the angles of a triangle using algebraic expressions. It covers the fundamental property that the sum of a triangle's angles is always 180 degrees. Two examples are provided: one where two angles are equal and the third is 30 degrees less, and another where the second angle is twice the first and the third is 30 degrees more than the second. The video demonstrates how to set up and solve equations to find the angles in each scenario.

What is the sum of the angles in any triangle?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

If two angles of a triangle are equal, and the third is 30 degrees less than the first, what is the measure of the third angle?

• 60 degrees

• 40 degrees

• 30 degrees

• 50 degrees

In the first example, if the first angle is x, how is the third angle represented algebraically?

• x

• 2x

• x - 30

• x + 30

What are the measures of the angles in the first example?

• 70, 70, 40

• 60, 60, 60

• 80, 80, 20

• 90, 45, 45

In the second example, how is the second angle related to the first?

• It is half the first

• It is twice the first

• It is equal to the first

• It is 30 degrees more than the first

If the second angle is twice the first, and the third is 30 degrees more than the second, how is the third angle represented algebraically?

• x + 30

• 3x

• x - 30

• 2x + 30

What are the measures of the angles in the second example?

• 30, 60, 90

• 45, 45, 90

• 30, 30, 120

• 60, 60, 60