Answer:
angle JKL is 22°
Explanation:
You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.
Exterior angle
The exterior angle is equal to the sum of the remote interior angles:
angle JKL = angle I + angle J
5x -3 = (2x +8) +(x -1)
5x -3 = 3x +7 . . . . . . . . . simplify
2x = 10 . . . . . . . . . . . add 3-3x
x = 5 . . . . . . . divide by 2
5x -3 = 5(5) -3 = 22 . . . . . degrees
Angle JKL is 22 degrees.
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Additional comment
It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.
The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.
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