Question

in △jkl, m∠j = 40 and m∠l is 3 times m∠k. find m∠k and m∠l.

Explanation:

Step1: Let \( m\angle K=x \)

Since \( m\angle L = 3m\angle K \), then \( m\angle L=3x \).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \( 180^{\circ} \). So \( m\angle J+m\angle K + m\angle L=180^{\circ} \).
Substitute \( m\angle J = 40^{\circ} \), \( m\angle K=x \), and \( m\angle L = 3x \) into the equation: \( 40+x + 3x=180 \).

Step3: Solve the equation for \( x \)

Combine like terms: \( 40+4x=180 \).
Subtract 40 from both sides: \( 4x=180 - 40=140 \).
Divide both sides by 4: \( x=\frac{140}{4}=35 \).

Step4: Find \( m\angle L \)

Since \( m\angle L = 3x \), substitute \( x = 35 \) into it. Then \( m\angle L=3\times35 = 105 \).

Answer:

\( m\angle K = 35 \), \( m\angle L=105 \)