Question

current skill $ show answer (2) request he 8 7 5x + 133 5 4x + 119 3 2 1 find the measure of angle 3. 4 game credits

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So \(5x + 133=4x + 119+180\) (because \(5x + 133\) and \(4x + 119\) are supplementary to the same - type of angles formed by the intersection of lines. Also, \(5x+133\) and the angle adjacent to \(4x + 119\) (which is \(180-(4x + 119)\)) are supplementary. Another way: Since \(5x + 133\) and \(4x+119\) are same - side exterior and interior angles (or we can use the property that \(5x + 133\) and \(4x + 119\) are related as \(5x+133+(4x + 119)=180\) (they are supplementary).

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Step2: Find the measure of \(4x + 119\)

Substitute \(x = 166\) into \(4x+119\).

$$4x+119=4\times166 + 119=664+119 = 783$$

(This is wrong. Let's start again. The correct relationship is that \(5x + 133\) and \(4x + 119\) are supplementary. So \(5x+133+4x + 119=180\))

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Step3: Find the measure of angle \(3\)

Angle \(3\) and \(4x + 119\) are supplementary. First, find \(4x+119\) when \(x=-8\).

$$4x + 119=4\times(-8)+119=-32 + 119 = 87$$

Since \(\angle3+(4x + 119)=180\) (linear - pair), then \(\angle3=180-(4x + 119)\)
\(\angle3 = 93^{\circ}\)

Answer:

\(93^{\circ}\)