Isosceles Triangle Angle Problems

The video tutorial explores solving for x in an isosceles triangle with given angle measures. It examines three scenarios based on the congruence of base angles and vertex angles, solving each to find possible values of x. The tutorial emphasizes understanding the properties of isosceles triangles and applying algebraic methods to solve geometric problems.

What are the given expressions for the angles in the isosceles triangle?

• 3x + 5 and x + 16

• 4x + 5 and x + 10

• 2x + 10 and x + 20

• x + 5 and 3x + 16

What is a key property of the base angles in an isosceles triangle?

• They are supplementary.

• They are complementary.

• They are congruent.

• They are always different.

In the first scenario, what is the equation formed by the angles?

• 3x + 5 + 3x + 5 + x + 16 = 180

• 2x + 10 + x + 20 = 180

• x + 5 + 3x + 16 = 180

• 4x + 5 + x + 10 = 180

What is the value of x in the first scenario?

• x = 26

• x = 24

• x = 22

• x = 20

In the second scenario, what equation is used to find x?

• 3x + 5 = x + 16

• 4x + 5 = x + 10

• 2x + 10 = x + 20

• x + 5 = 3x + 16

What is the value of x in the second scenario?

• x = 11/2

• x = 6

• x = 5.5

• x = 7

In the third scenario, what is the equation formed by the angles?

• x + 16 + x + 16 + 3x + 5 = 180

• 2x + 10 + x + 20 = 180

• 4x + 5 + x + 10 = 180

• x + 5 + 3x + 16 = 180

What is the value of x in the third scenario?

• x = 28.6

• x = 143/5

• x = 30

• x = 32

How many possible values of x are there based on the given scenarios?

• Two

• Four

• One

• Three

Which of the following is not a possible value of x?

• 143/5

• 30

• 11/2

• 22