Question

what is the measure of \\( \angle 2 \\) in degrees?
the measure of \\( \angle 1 \\) is \\( (10 x+8) \\) and the measure of \\( \angle 3 \\) is \\( (12 x-10) \\).

Explanation:

Step1: Find the value of \(x\)

Since \(\angle1=(10x + 8)^{\circ}\) and \(\angle3=(12x-10)^{\circ}\), and \(\angle1\) and \(\angle3\) are vertical angles, so \(\angle1=\angle3\).

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Step2: Calculate \(\angle1\)

Substitute \(x = 9\) into \(\angle1=(10x + 8)^{\circ}\), we get \(\angle1=(10\times9+8)^{\circ}=98^{\circ}\).

Step3: Calculate \(\angle2\)

Because \(\angle1\) and \(\angle2\) are supplementary angles (\(\angle1+\angle2 = 180^{\circ}\)), so \(\angle2=180^{\circ}-\angle1\).

$$ \angle2=180^{\circ}-98^{\circ}=82^{\circ} $$

Answer:

\(82\)