Question

determining an unknown angle measure

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

Explanation:

Step1: Use vertical - angle and parallel - line properties

Since \(q\parallel s\) and \(r\) is a transversal, \(\angle6\) and \(\angle8\) are supplementary (\(\angle6+\angle8 = 180^{\circ}\)).
So, \((2x - 5)+(x + 5)=180\).

Step2: Solve the equation for \(x\)

Simplify the left - hand side of the equation: \(2x-5+x + 5=3x\).
Then \(3x=180\), so \(x = 60\).

Step3: Find \(m\angle6\)

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

Step4: Use the property of vertical angles

\(\angle3\) and \(\angle6\) are vertical angles. Vertical angles are equal.

Answer:

\(115\)