Respuesta :

Based on the information about side JK = side JL, then we know it is at least an isosceles triangle. Furthermore, ∡K =∡L because they are the base angles in an isosceles triangle.
Equation: 4x - 1 = 9x - 31
Solved: x = 6
Angle measures: ∡J = 23(6) - 4 = 138 - 4= 134
                            ∡K = ∡L = 23

m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° is the answer.    

    From the figure attached,

  • JK and JL are equal sides of the triangle.
  • m(∠J) = 23x - 4
  • m(∠K) = 4x - 1
  • m(∠L) = 9x - 31

Since, two sides JK and JL of ΔJKL are equal in measure,

Therefore, ΔJKL is an isosceles triangle.

  By the property of an isosceles triangle, opposite angles of the equal sides are equal.

Therefore, m(∠K) = m(∠L)

4x - 1 = 9x - 31

9x - 4x = 31 - 1

5x = 30

x = 6

  By substituting the value of 'x' in the measures of each angle,

m(∠J) = 23x - 4

         = 23(6) - 4

         = 138 - 4

         = 134°

m(∠K) = 4x - 1

          = 4(6) - 1

          = 24 - 1

          = 23°

m(∠L) = 9x - 31

          = 9(6) - 31

          = 23°

      Therefore, m(∠J) = 134°, m(∠K) = 23° and m(∠L) = 23° will be the answer.

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