Question

m∠6 is (2x - 5)° and m∠8 is (x + 5)°. what is m∠3?

Explanation:

Step1: Find the value of \(x\)

Since \(\angle6\) and \(\angle8\) are supplementary angles (they form a linear pair), we have \((2x - 5)+(x + 5)=180\).
Simplifying the left - hand side: \(2x-5+x + 5=3x\). So, \(3x=180\), and \(x = 60\).

Step2: Find \(m\angle6\)

Substitute \(x = 60\) into the expression for \(m\angle6\): \(m\angle6=(2x - 5)=(2\times60-5)=115^{\circ}\).

Step3: Use the property of parallel lines

Since \(q\parallel s\) and \(r\) is a transversal, \(\angle3\) and \(\angle6\) are alternate interior angles. Alternate interior angles are congruent when two parallel lines are cut by a transversal. So, \(m\angle3=m\angle6\).

Answer:

\(115\)