Question

what is the measure of ∠l? (9x - 24)° (x + 9)° (6x - 5)°

Explanation:

Step1: Use exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(9x - 24=(x + 9)+(6x - 5)\).

Step2: Simplify the equation

Simplify the right - hand side: \((x + 9)+(6x - 5)=x+6x + 9 - 5=7x + 4\). The equation becomes \(9x-24 = 7x+4\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(9x-7x-24=7x - 7x+4\), which gives \(2x-24 = 4\). Then add \(24\) to both sides: \(2x=4 + 24\), so \(2x=28\). Divide both sides by \(2\): \(x = 14\).

Step4: Find the measure of \(\angle L\)

Substitute \(x = 14\) into the expression for \(\angle L\) (\(\angle L=(x + 9)^{\circ}\)). So \(\angle L=(14 + 9)^{\circ}=23^{\circ}\).

Answer:

\(23^{\circ}\)