All possible values of x are 28.8 and [tex]22\frac{2}{7}[/tex]
Step-by-step explanation:
In any isosceles triangle
- Two sides are equal in length
- The angle between the two equal sides is called the vertex angle
- The two other angles are called base angles
Case 1:
∵ The measure of the vertex angle is (3x + 4)°
∵ The measure of each base angle is (x + 16)°
∵ The measures of the interior angles of a triangle is 180°
- Equate the sum of the angles by 180
∴ (3x + 4) + (x + 16) + (x + 16) = 180
- Add like terms
∴ (3x + x + x) + (4 + 16 + 16) = 180
∴ 5x + 36 = 180
- Subtract 36 from both sides
∴ 5x = 144
- Divide both sides by 5
∴ x = 28.8
Case 2:
∵ The measure of the vertex angle is (x + 16)°
∵ The measure of each base angle is (3x + 4)°
∵ The measures of the interior angles of a triangle is 180°
- Equate the sum of the angles by 180
∴ (x + 16) + (3x + 4) + (3x + 4) = 180
- Add like terms
∴ (x + 3x + 3x) + (16 + 4 + 4) = 180
∴ 7x + 24 = 180
- Subtract 24 from both sides
∴ 7x = 156
- Divide both sides by 7
∴ x = [tex]22\frac{2}{7}[/tex]
All possible values of x are 28.8 and [tex]22\frac{2}{7}[/tex]
Learn more:
You can learn more about triangles in brainly.com/question/6530759
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