x=6
m∠K = 23º
m∠L = 23º
m∠J =138º
1) Let's visualize it to better understand that
2) Since it is an isosceles triangle (at least 2 congruent sides and two congruent angles) then we can write that
m∠K ≅ m∠L
4x -1 = 9x -31
4x -9x = -31 +1
-5x = -30
5x = 30
x= 6
Plugging into one of those congruent angles:
m∠K = 4(6) -1 = 23º
m∠K ≅ m∠L
Then m∠L = 23º
Since the sum of the interior angles in any triangle is equal to 180º, we can write
Δ JKL = 23 +23 + (23x -4) = 180º
m∠J = 23x -4 =23(6) -4 =138º
m∠J =138º
3) So the answer is
x=6
m∠K = 23º
m∠L = 23º
m∠J =138º
