Question

find the measure of ∠gmj. m∠gmj =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, \(12x - 1=13x - 44\).

Step2: Solve for \(x\)

Subtract \(12x\) from both sides: \(-1=x - 44\). Then add 44 to both sides, getting \(x = 43\).

Step3: Find the measure of \(\angle GMJ\)

Substitute \(x = 43\) into the expression for \(\angle GMJ\) which is \(12x-1\). So, \(m\angle GMJ=12\times43 - 1=516 - 1=515\) is incorrect. Since the angles are likely supplementary (linear - pair), we assume \(12x - 1+13x - 44 = 180\) (because they form a straight - line).

Step4: Solve the new equation for \(x\)

Combine like terms: \(25x-45 = 180\). Add 45 to both sides: \(25x=225\). Divide both sides by 25, we get \(x = 9\).

Step5: Calculate the measure of \(\angle GMJ\)

Substitute \(x = 9\) into the expression for \(\angle GMJ\): \(m\angle GMJ=12x - 1=12\times9-1=108 - 1 = 107\).

Answer:

\(107\)