Question

find ( mangle acb ).

Explanation:

Step1: Use the property of parallel lines and transversal

Since the lines are parallel, \((7x - 2)+(8x + 13)=180\) (supplementary angles).

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Step2: Find \(m\angle ACB\)

We know that in a triangle, the sum of angles is \(180^{\circ}\). Also, using the property of alternate - interior angles (because of parallel lines).
\(m\angle ACB=180-(82+(7x - 2))\)
Substitute \(x = 11\) into \(7x-2\), we get \(7\times11-2=75^{\circ}\)
\(m\angle ACB=180-(82 + 75)=23^{\circ}\)

Answer:

\(x = 11\), \(m\angle ACB=23^{\circ}\)