Question

find m∠1
(3x + 6)°
123°
1
m∠1 =
(type an integer or a fraction. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify vertical angles

The angle of \(123^\circ\) and \((3x + 6)^\circ\) are vertical angles, so they are equal. Thus, \(3x + 6 = 123\).

Step2: Solve for x

Subtract 6 from both sides: \(3x = 123 - 6 = 117\). Then divide by 3: \(x=\frac{117}{3}=39\).

Step3: Find \(m\angle1\)

\(\angle1\) and \((3x + 6)^\circ\) are supplementary (linear pair), so \(m\angle1 + (3x + 6)=180\). Substitute \(x = 39\): \(3x+6 = 3\times39 + 6 = 123\). Then \(m\angle1=180 - 123 = 57\).

Answer:

57