Question

current skill $ show answer (2) re 3x + 104 1 4 3 8x + 186 6 8 7 find the measure of angle 3.

Explanation:

Step1: Use vertical - angle property

Since \(3x + 104\) and \(8x+186\) are vertical angles, \(3x + 104=8x + 186\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(104 = 5x+186\).
Subtract \(186\) from both sides: \(5x=104 - 186=-82\).
Divide by \(5\): \(x =-\frac{82}{5}=- 16.4\).

Step3: Find the measure of \(3x + 104\)

Substitute \(x=-16.4\) into \(3x + 104\): \(3\times(-16.4)+104=-49.2 + 104 = 54.8\).

Step4: Use the property of adjacent angles (linear - pair)

Since \(\angle3\) and \(3x + 104\) form a linear - pair (\(\angle3+(3x + 104)=180^{\circ}\)), \(\angle3=180-(3x + 104)\).
Substitute \(x =-16.4\): \(\angle3=180 - 54.8=125.2^{\circ}\).

Answer:

\(125.2^{\circ}\)