Question

find m∠1
m∠1=□
(type an integer or a fraction. do not include the degree symbol in your answer)

Explanation:

Step1: Find the value of \(x\)

Since \(123^{\circ}\) and \((3x + 6)^{\circ}\) are vertical angles, they are equal. So \(3x+6 = 123\).
Subtract \(6\) from both sides: \(3x=123 - 6=117\).
Divide both sides by \(3\): \(x=\frac{117}{3}=39\).

Step2: Find \(m\angle1\)

\(m\angle1\) and \((3x + 6)^{\circ}\) are supplementary angles (they form a linear - pair).
Substitute \(x = 39\) into \((3x + 6)\): \(3x+6=3\times39 + 6=117+6 = 123\).
Since \(m\angle1+(3x + 6)=180^{\circ}\), then \(m\angle1=180-(3x + 6)\).
Substitute \(3x + 6 = 123\) into the equation: \(m\angle1=180 - 123=57\).

Answer:

\(57\)