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

Step2: Solve for \(x\)

Subtract 6 from both sides:
\(3x = 123 - 6 = 117\)
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 \(x = 39\): \(3(39) + 6 = 123\).
Thus, \(m\angle1 = 180 - 123 = 57\).

Answer:

57