Question

the measure of angle jkl can be represented using the expression 3x + 5. what is the degree measure of ∠jkl?

Explanation:

Step1: Use the exterior - angle property

The exterior - angle property of angles formed by a transversal and two lines (here, the property for angles in the given geometric figure). We know that \(3x + 5=45 + x\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation:
\(3x+5 - x=45 + x-x\)
\(2x+5 = 45\)
Subtract 5 from both sides:
\(2x+5 - 5=45 - 5\)
\(2x=40\)
Divide both sides by 2:
\(x = 20\)

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

Substitute \(x = 20\) into the expression \(3x + 5\).
\(3x+5=3\times20 + 5\)
\(=60 + 5\)
\(=65\)

Answer:

\(65\)