Question

1. look at the figure. find the value of x.

figure of a quadrilateral with right angles at k and m, jl as a common side, jk = x + 5, jm = 2x - 7, and angle at l is equal for both triangles

options:
10
17
24
12

Explanation:

Step1: Identify congruent triangles

Triangles \( \triangle KLJ \) and \( \triangle MLJ \) are right triangles, share hypotenuse \( JL \), and \( \angle KLJ = \angle MLJ \) (marked equal). So, \( \triangle KLJ \cong \triangle MLJ \) (AAS or HL). Thus, \( JK = JM \).

Step2: Set up equation

Given \( JK = x + 5 \) and \( JM = 2x - 7 \), set \( x + 5 = 2x - 7 \).

Step3: Solve for x

Subtract \( x \) from both sides: \( 5 = x - 7 \). Add 7 to both sides: \( x = 12 \).

Answer:

12