Question

5.
find the value of x _
find the m∠jlk _

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, \(7x + 4+9x=100\).

Step2: Combine like terms

Combine the \(x\) terms: \((7x + 9x)+4 = 100\), which simplifies to \(16x+4 = 100\).

Step3: Solve for \(x\)

Subtract \(4\) from both sides: \(16x+4−4 = 100−4\), so \(16x=96\).
Divide both sides by \(16\): \(x=\frac{96}{16}=6\).

Step4: Find \(m\angle JLK\)

Since \(\angle JLK\) and the \(100^{\circ}\) angle are supplementary (they form a linear pair), \(m\angle JLK = 180 - 100=80^{\circ}\).

Answer:

The value of \(x\) is \(6\). The measure of \(\angle JLK\) is \(80^{\circ}\).