Question

what is the value of u?
diagram: points j, g, h, i; right angles at i (between line i and segment ji) and at g (between segment jg and line g); segment ji labeled ( u + 54 ), segment jg labeled ( 4u ); angle at h with two arcs (possibly angle bisector).
( u = ) blank
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Explanation:

Step1: Identify angle relationship

The two angles \( u + 54 \) and \( 4u \) are equal because they are the angles between a common side and two perpendicular lines (so they are congruent). So we set up the equation: \( u + 54 = 4u \)

Step2: Solve for \( u \)

Subtract \( u \) from both sides: \( 54 = 4u - u \)
Simplify: \( 54 = 3u \)
Divide both sides by 3: \( u=\frac{54}{3} \)
Calculate: \( u = 18 \)

Answer:

\( 18 \)