Question

What is the value of x?

Answer 1

This is an equilateral triangle, which is a triangle that has 3 congruent/equal sides and 3 congruent angles.

To find "x", you can set the sides equal to each other because they are suppose to be the same length (you can just do two sides because all of the sides are the same)

[Side AB = Side BC]

4x - 10 = 3x + 2     Subtract 3x on both sides

x - 10 = 2         Add 10 on both sides

x = 12

[proof]

Side AB:

4x - 10    Plug in 12 for x

4(12) - 10 = 48 - 10 = 38

Side BC:

3x + 2     Plug in 12 for x

3(12) + 2 = 36 + 2 = 38

Side AC:

5x - 22      Plug in 12 for x

5(12) - 22 = 60 - 22 = 38

This is also an equilateral triangle (the tick marks show that the sides are the same)

A triangle is 180°. So the three angles add up to 180°.

Since this is an equilateral triangle, all the angles should be the same.

Each angle is 60°

[60° + 60° + 60° = 180°   or you could have divided 180 by 3 = 60]

Now that you know each angle is 60°, you can do:

(2x - 4)° = 60°

2x - 4 = 60    Add 4 on both sides

2x = 64    Divide 2 on both sides

x = 32