Question

find m∠cab.

Explanation:

Step1: Use the property of alternate - interior angles

Since \(DE\parallel BF\), the alternate - interior angles are equal. So, \(11x - 33=4x + 23\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(11x-4x - 33=4x-4x + 23\), which gives \(7x-33 = 23\).
Add \(33\) to both sides: \(7x-33 + 33=23 + 33\), so \(7x=56\).
Divide both sides by \(7\): \(x=\frac{56}{7}=8\).

Step3: Calculate \(m\angle CAB\)

Substitute \(x = 8\) into \(4x + 23\). Then \(m\angle CAB=4\times8+23\).
\(m\angle CAB=32 + 23=55^{\circ}\).

Answer:

\(55^{\circ}\)