Question

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

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So \(123^{\circ}=(3x + 6)^{\circ}\).

Step2: Solve for \(x\)

$$
LATEXBLOCK0
$$

Step3: Use the property of adjacent - supplementary angles

\(\angle1\) and \((3x + 6)^{\circ}\) are adjacent - supplementary angles. So \(m\angle1+(3x + 6)=180\). Substitute \(x = 39\) into \((3x + 6)\), we get \((3\times39+6)=123\). Then \(m\angle1=180-(3x + 6)=180 - 123\).

Answer:

\(57\)