Question

part 1 of 2
find the angle of rotation for the rotation that is the composition ( l_{1} circ l_{2} ). then, draw the image.
the angle of rotation is ( square^{circ} ).
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question 14 of 20 back next

Explanation:

Step1: Recall the property of rotation angle in composition of reflections

The angle of rotation for the composition of two reflections \(r_{m}\circ r_{l}\) about two intersecting lines \(l\) and \(m\) is \(2\theta\), where \(\theta\) is the angle between the two lines \(l\) and \(m\).

Step2: Determine the angle between the two lines

From the figure, the angle between the two lines \(l\) and \(m\) is \(74^{\circ}\).

Step3: Calculate the angle of rotation

Using the formula \(2\theta\), substitute \(\theta = 74^{\circ}\). So the angle of rotation is \(2\times74^{\circ}=148^{\circ}\)

Answer:

\(148\)