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

Step2: Find \(m\angle6\)

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

Step3: Use the property of corresponding angles

\(\angle3\) and \(\angle6\) are corresponding angles (because \(q\parallel s\) and \(r\) is a transversal).
So \(m\angle3=m\angle6\).

Answer:

\(115\)