To find the degree measure of each angle in the triangle provided, we can use the angle sum property of a triangle, which states that the sum of the interior angles of a triangle is always 180 degrees.
Given:
- m∠ZH = x + 8
- m∠Z1 = 6x - 4
- m∠ZJ = 4x
We need to find the values of x for each angle and then calculate the degree measure of each angle.
1. Set up the equation using the angle sum property of a triangle:
(x + 8) + (6x - 4) + 4x = 180
2. Simplify the equation and solve for x:
x + 8 + 6x - 4 + 4x = 180
11x + 4 = 180
11x = 176
x = 16
3. Substitute the value of x back into the expressions for each angle:
- m∠ZH = x + 8 = 16 + 8 = 24 degrees
- m∠Z1 = 6x - 4 = 6(16) - 4 = 92 degrees
- m∠ZJ = 4x = 4(16) = 64 degrees
Therefore, the degree measure of each angle in the triangle is:
- ∠ZH = 24 degrees
- ∠Z1 = 92 degrees
- ∠ZJ = 64 degrees
