Question

current skill $ show answer (2) request help 1 2 3 6x + 24 5 6 7 5x + 34 find the measure of angle 2

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So \(6x + 24=5x + 34\)

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(6x-5x+24 = 5x-5x + 34\), which gives \(x+24=34\). Then subtract \(24\) from both sides: \(x=34 - 24=10\)

Step3: Find angle \(2\)

First, find \(6x + 24\) when \(x = 10\). \(6\times10+24=60 + 24=84\). Angles \(1\), \(2\) and \(6x + 24\) form a straight - line (sum to \(180^{\circ}\)). Let's assume angle \(1\) and angle \(3\), angle \(5\) and angle \(7\) etc. But since \(6x + 24\) and angle \(5\) are vertical angles, and angles \(1\), \(2\) and \(6x + 24\) are adjacent angles on a straight - line. Also, if we consider the fact that \(6x + 24\) and angle \(5\) are vertical angles, and angles around the intersection. Another way: since \(6x+24 = 84\), and angles \(1\), \(2\) and the angle equal to \(6x + 24\) (because of vertical angles) form a triangle - like (sum to \(180^{\circ}\)). But more simply, angles \(1\), \(2\) and the angle with measure \(6x + 24\) are adjacent angles on a straight - line. If we assume that the lines are intersected and we use the linear - pair property. Let's assume that the angle adjacent to angle \(2\) (the one with measure \(6x + 24\)) and angle \(2\) form a linear pair. Wait, no, actually, when two lines intersect, the sum of adjacent angles is \(180^{\circ}\). If we consider the intersection of the lines, and assume that the angle with measure \(6x + 24\) and angle \(2\) are adjacent. Wait, no, actually, when we have two intersecting lines, we know that \(6x+24\) (after \(x = 10\), it is \(84\)) and angle \(2\) are supplementary (because they are adjacent angles formed by the intersection of two lines). So \(\angle2=180-(6x + 24)\). Substitute \(x = 10\): \(\angle2=180 - 84=96\)

Answer:

\(96\)