The sum of the measures of the three angles of a triangle is 180 the angles are 2x-4, x, x+6

Mathematics

1 answer:

Oksanka [162]3 years ago

4 0

The value of x is 44.5

The measures of the three angles are 85° , 44.5° , 50.5°

Step-by-step explanation:

The sum of the measures of the three angles of a triangle is 180°

The angles of a triangle are 2x - 4 , x , x + 6

We need to find the value of x and the measure of each angle

To solve the problem

Add the three angles
Equate their sum by 180
Solve the equation to find the value of x
Substitute the value of x in each angle to find its measure

∵ The angles of the triangles are 2x - 4 , x , x + 6

∴ The sum of the angles = 2x - 4 + x + x + 6

- Add the like terms

∴ The sum of the angles = 4x + 2

∵ The sum of the measures of the three angles of a triangle is 180°

- Equate the sum of the angles by 180

∴ 4x + 2 = 180

- Subtract 2 from both sides

∴ 4x = 178

- Divide both sides by 4

∴ x = 44.5

The value of x is 44.5

Substitute the value of x in each angle to find the measure of each angle

∵ The measure of one angle = 2x - 4

∵ x = 44.5

∴ The measure of the angle = 2(44.5) - 4 = 85°

∵ The measure of 2nd angle = x

∴ The measure of the angle = 44.5°

∵ The measure of one angle = x + 6

∵ x = 44.5

∴ The measure of the angle = 44.5 + 6 = 50.5°

The measures of the three angles are 85° , 44.5° , 50.5°

Learn more:

You can learn more about the angles of a triangle in brainly.com/question/4302397

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