Answer:
m < I = 80°
m < J = 50°
m < K = 50°
Step-by-step explanation:
Given the isoceles triangle, IJK, where:
m < J = (2x + 38)°
m < K = (4x + 26)°
In order to solve for x, we can establish the following equality statement:
m < J = m < K
(2x + 38)° = (4x + 26)°
2x + 38 = 4x + 26
Subtract 2x from both sides:
2x - 2x + 38 = 4x - 2x + 26
Subtract 26 from both sides:
38 - 26 = 2x + 26 - 26
12 = 2x
Divide both sides by 2:
12/2 = 2x/2
6 = x
Substitute the value of x into the equality statement:
m < J = m < K
(2x + 38)° = (4x + 26)°
2(6) + 38 = 4(6) + 26
12 + 38 = 24 + 26
50° = 50°
Therefore, m < J = 50°, and m < K = 50°. To find m < I:
m < I = 180° - (m < J + m < K)°
m < I = 180 - (50° + 50°)
m < I = 180° - 100°
m < I = 80°
Therefore, the correct answers are:
m < I = 80°
m < J = 50°
m < K = 50°
