Question

The measures of two angles of an isosceles triangle are 3x + 4 and x + 16. Find all possible values of x

Answer 1

All possible values of x are 28.8 and $22\frac{2}{7}$

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 = $22\frac{2}{7}$

All possible values of x are 28.8 and $22\frac{2}{7}$

Learn more:

You can learn more about triangles in brainly.com/question/6530759

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