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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