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 supplementary angles (they form a linear pair along a transversal intersecting parallel lines), we have the equation \(123+(3x + 6)=180\).

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Step2: Find \(m\angle1\)

\(\angle1\) and \((3x + 6)^{\circ}\) are alternate - interior angles (because of the parallel lines and transversal). When \(x = 17\), \((3x+6)^{\circ}=(3\times17 + 6)^{\circ}=(51 + 6)^{\circ}=57^{\circ}\). So \(m\angle1=(3x + 6)^{\circ}\) (alternate - interior angles are equal).

Answer:

\(57\)