Question

hijk ~ vuxw. what are ( mangle k ) and ( mangle u )?
( mangle k=) ( ^{circ})
( mangle u=) ( ^{circ})

Explanation:

Step1: Use the property of similar polygons

Similar polygons have corresponding angles equal.

Step2: Find \(m\angle K\)

Since \(HIJK\sim VUXW\), \(\angle K\) corresponds to \(\angle X\). So \(m\angle K = 97^{\circ}\)

Step3: Find the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\)
For quadrilateral \(HIJK\), let \(m\angle J=x\). Then \(60^{\circ}+89^{\circ}+97^{\circ}+x = 360^{\circ}\), \(x=360-(60 + 89+97)=114^{\circ}\)
For quadrilateral \(VUXW\), \(\angle U\) corresponds to \(\angle I\)

Step4: Calculate \(m\angle U\)

Since \(\angle I = 89^{\circ}\) (from \(HIJK\)) and \(\angle U\) corresponds to \(\angle I\) (because \(HIJK\sim VUXW\)), so \(m\angle U=89^{\circ}\)

Answer:

\(m\angle K = 97^{\circ}\)
\(m\angle U = 89^{\circ}\)