Question

determining an unknown angle measure

$m\angle 6$ is $(2x - 5)^{circ}$ and $m\angle 8$ is $(x + 5)^{circ}$.

what is $m\angle 3$?

Explanation:

Step1: Use the property of vertical angles

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

Step2: Solve the equation for \(x\)

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

Step3: Find \(m\angle6\)

Substitute \(x = 60\) into \(m\angle6=(2x - 5)^{\circ}\).
\(m\angle6=(2\times60 - 5)^{\circ}=(120 - 5)^{\circ}=115^{\circ}\).

Step4: Use the property of corresponding angles

Since \(q\parallel s\) and \(r\) is a transversal, \(m\angle3=m\angle6\) (corresponding angles).

Answer:

\(115^{\circ}\)