Question

determine the measure of angle j.
m∠j=□°

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. So, \(j=(5x - 3)+(4x - 2)\), and also \(j = 180-(10x - 20)\) (since \(j\) and \(10x - 20\) are supplementary).

Since \((5x - 3)+(4x - 2)=180-(10x - 20)\)

First, simplify the left - hand side: \((5x+4x)+(-3 - 2)=9x - 5\)

Simplify the right - hand side: \(180-10x + 20=200-10x\)

So, \(9x - 5=200-10x\)

Step2: Solve for \(x\)

Add \(10x\) to both sides: \(9x+10x - 5=200-10x+10x\), which gives \(19x - 5=200\)

Add \(5\) to both sides: \(19x-5 + 5=200 + 5\), so \(19x=205\)

Divide both sides by \(19\): \(x = 15\)

Step3: Find the measure of \(j\)

Since \(j=(5x - 3)+(4x - 2)=9x - 5\)

Substitute \(x = 15\) into \(9x - 5\): \(9\times15-5=135 - 5=70\)

Answer:

\(70\)