Question

12,891 Learners found this answer helpful

what is the value of u?
h
u+18
i
7u
k
42°
42°
j
u =
submit

Explanation:

Step1: Identify congruent angles and sides

Since \( \angle K \) and \( \angle I \) are right angles, and \( \angle HJK = \angle HJI = 42^\circ \), triangles \( HJK \) and \( HIJ \) are congruent (AAS or ASA). Thus, \( HK = HI \).

Step2: Set up the equation

Given \( HK = 7u \) and \( HI = u + 18 \), we set \( 7u = u + 18 \).

Step3: Solve for \( u \)

Subtract \( u \) from both sides: \( 7u - u = 18 \) → \( 6u = 18 \). Divide by 6: \( u = \frac{18}{6} = 3 \).

Answer:

\( u = 3 \)