Question

find m∠1. m∠1= 57 (type an integer or a fraction. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify supplementary angles

The angle of \(123^\circ\) and \((3x + 6)^\circ\) are supplementary (they form a linear pair), so \(123+(3x + 6)=180\).

Step2: Solve for x (optional, but check)

Simplify: \(3x+129 = 180\), \(3x=51\), \(x = 17\). Then \(3x + 6=3(17)+6 = 57\). Also, \(\angle1\) and \((3x + 6)^\circ\) are vertical angles or \(\angle1\) is supplementary to \(123^\circ\) (since \(\angle1 + 123=180\) as they are a linear pair). So \(m\angle1=180 - 123=57\).

Answer:

57