Question

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

Explanation:

Step1: Set up the angle sum equation

The sum of \( \angle JKL \) and \( \angle LKM \) is equal to \( \angle JKM \). So we have the equation: \( 4x + (2x - 10) = 140 \).

Step2: Solve for \( x \)

Combine like terms: \( 4x + 2x - 10 = 140 \) simplifies to \( 6x - 10 = 140 \). Add 10 to both sides: \( 6x = 150 \). Divide both sides by 6: \( x = 25 \).

Step3: Find \( m\angle JKL \)

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

Step4: Find \( m\angle LKM \)

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

Answer:

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