Question

find ( mangle jkl ) and ( mangle lkm ) if ( mangle jkm = 140^{circ} ).

( mangle jkl=)
( mangle lkm=)

Explanation:

Step1: Set up the equation

Since \(m\angle JKM=m\angle JKL + m\angle LKM\), we have \(4x+(2x - 10)=140\).

Step2: Simplify the equation

Combine like - terms: \(4x+2x-10 = 140\), which becomes \(6x-10=140\).

Step3: Solve for \(x\)

Add \(10\) to both sides: \(6x=140 + 10=150\). Then divide by \(6\): \(x=\frac{150}{6}=25\).

Step4: Find \(m\angle JKL\)

Substitute \(x = 25\) into \(m\angle JKL=4x\). So \(m\angle JKL=4\times25 = 100^{\circ}\).

Step5: Find \(m\angle LKM\)

Substitute \(x = 25\) into \(m\angle LKM=(2x - 10)\). So \(m\angle LKM=2\times25-10=50 - 10=40^{\circ}\).

Answer:

\(m\angle JKL = 100^{\circ}\)
\(m\angle LKM=40^{\circ}\)