Question

1. $\angle m$ and $\angle n$ are supplementary and $m\angle m = 37^\circ$. if $m\angle n = (13x)^\circ$, what is the value of $x$ and the $m\angle n$?

a. equation: _____________

b. $x = $ ____ $m\angle m$ __ $m\angle n$ ____

Explanation:

Part a: Equation

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\). So, \(m\angle M + m\angle N = 180^\circ\).

Step2: Substitute given values

We know \(m\angle M = 37^\circ\) and \(m\angle N = (13x)^\circ\). Substituting these into the equation gives \(37 + 13x = 180\).

Step1: Solve for \(x\)

Start with the equation \(37 + 13x = 180\). Subtract \(37\) from both sides: \(13x = 180 - 37\). Calculate \(180 - 37 = 143\), so \(13x = 143\). Then divide both sides by \(13\): \(x = \frac{143}{13}\).

Step2: Calculate \(x\)

\(\frac{143}{13} = 11\), so \(x = 11\).

Step3: Find \(m\angle N\)

Since \(m\angle N = 13x^\circ\) and \(x = 11\), substitute \(x\): \(m\angle N = 13 \times 11\). Calculate \(13 \times 11 = 143\), so \(m\angle N = 143^\circ\). Also, \(m\angle M\) is given as \(37^\circ\).

Answer:

\(37 + 13x = 180\)

Part b: Solve for \(x\) and \(m\angle N\)