Question

solve for k, if the measure of ∠jml is 130°. the diagram shows point m with three rays: ( overrightarrow{mj} ), ( overrightarrow{mk} ), and ( overrightarrow{ml} ). ( angle jmk = (2k + 33)^circ ) and ( angle kml = (-6k + 117)^circ ), with ( angle jml = 130^circ ).

Explanation:

Step1: Set up angle sum equation

The measure of \( \angle JML \) is the sum of \( (2k + 33)^\circ \) and \( (-6k + 117)^\circ \), so:
\( (2k + 33) + (-6k + 117) = 130 \)

Step2: Simplify left - hand side

Combine like terms:
\( 2k - 6k+33 + 117=130 \)
\( - 4k+150 = 130 \)

Step3: Solve for k

Subtract 150 from both sides:
\( -4k=130 - 150 \)
\( -4k=-20 \)
Divide both sides by - 4:
\( k=\frac{-20}{-4}=5 \)

Answer:

\( k = 5 \)