Question

1. in triangle jkl, angle j is (x + 8)°, angle l is (2x - 3)°, and the exterior angle at k is (6x - 5)°. find the value of x, angle j, and angle l.

Explanation:

Step1: Sum of triangle angles = 180°

$$(x+8) + (6x-5) + (2x-3) = 180$$

Step2: Simplify left side

$$9x + 0 = 180$$

Step3: Solve for x

$$x = \frac{180}{9} = 20$$

Step4: Calculate ∠J

$$\angle J = (20 + 8)^\circ = 28^\circ$$

Step5: Calculate ∠K

$$\angle K = (6\times20 - 5)^\circ = 115^\circ$$

Step6: Calculate ∠L

$$\angle L = (2\times20 - 3)^\circ = 37^\circ$$

Answer:

$\angle J=28^\circ$, $\angle K=115^\circ$, $\angle L=37^\circ$