Question

if m∠lrk = 84°, then what is m∠jrm?
answer attempt 1 out of 3
m∠jrm = submit answer

Explanation:

Step1: Find the measure of \(\angle2\)

Vertical angles are equal. \(\angle1\) and \(\angle2\) are vertical angles. But we know that \(\angle LRK=\angle1 + \angle2\) and \(\angle1=\angle2\) (vertical angles). Wait, no, actually \(\angle LRK\) and \(\angle1\) are adjacent angles forming a linear - pair with \(\angle2\). Wait, no, \(\angle LRK\) and \(\angle2\) are vertical angles. Wait, no, \(\angle LRK\) and \(\angle1\) are adjacent. Wait, \(\angle LRK\) and \(\angle2\) are vertical angles. So \(m\angle2 = 84^{\circ}\)

Step2: Use the linear - pair relationship for \(\angle JRM\) and \(\angle2\)

\(\angle JRM\) and \(\angle2\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). Let \(x = m\angle JRM\). Then \(x+\angle2=180^{\circ}\)
Substitute \(\angle2 = 84^{\circ}\) into the equation: \(x+84^{\circ}=180^{\circ}\)
Solve for \(x\): \(x=180^{\circ}- 84^{\circ}\)

Answer:

\(96\)