Answer:
The equation to find [tex]x[/tex] is [tex](5\cdot x - 2)^{\circ} + (2\cdot x -2)^{\circ} + x^{\circ} = 180^{\circ}[/tex].
The degree measure of each angle is: [tex]m\angle J = 113^{\circ}[/tex], [tex]m\angle K = 44^{\circ}[/tex] and [tex]m\angle L = 23^{\circ}[/tex].
Step-by-step explanation:
From Euclidean Geometry we remember that the sum of internal angles in triangles equals 180°. If we know that [tex]m\angle J = (5\cdot x -2)^{\circ}[/tex], [tex]m \angle K = (2\cdot x - 2)^{\circ}[/tex] and [tex]m\angle L = x^{\circ}[/tex], then we construct the following equation of the triangle JKL in function of [tex]x[/tex]:
[tex]m\angle J + m\angle K + m\angle L = 180^{\circ}[/tex] (1)
[tex](5\cdot x - 2)^{\circ} + (2\cdot x -2)^{\circ} + x^{\circ} = 180^{\circ}[/tex]
[tex]8\cdot x -4 = 180^{\circ}[/tex]
[tex]8\cdot x = 184[/tex]
[tex]x = 23[/tex]
Finally, the measure of each angle is, respectively:
[tex]m\angle J = (5\cdot x -2)^{\circ}[/tex]
[tex]m\angle J = 113^{\circ}[/tex]
[tex]m \angle K = (2\cdot x - 2)^{\circ}[/tex]
[tex]m\angle K = 44^{\circ}[/tex]
[tex]m\angle L = x^{\circ}[/tex]
[tex]m\angle L = 23^{\circ}[/tex]
