Question

1. in δjkl, if m∠l is thirteen more than m∠k and m∠j is seven more than six times m∠k, find the measure of each angle.

m∠j = _____
m∠k = _____
m∠l = _____

Explanation:

Step1: Define variables

Let \( m\angle K = x \). Then \( m\angle L = x + 13 \) and \( m\angle J = 6x + 7 \).

Step2: Use triangle angle sum

The sum of angles in a triangle is \( 180^\circ \), so \( x+(x + 13)+(6x + 7)=180 \).

Step3: Simplify the equation

Combine like terms: \( 8x+20 = 180 \).

Step4: Solve for \( x \)

Subtract 20: \( 8x=160 \), then divide by 8: \( x = 20 \).

Step5: Find each angle

• \( m\angle K=x = 20^\circ \)
• \( m\angle L=x + 13=20 + 13 = 33^\circ \)
• \( m\angle J=6x + 7=6(20)+7 = 127^\circ \)

Answer:

\( m\angle J = 127^\circ \), \( m\angle K = 20^\circ \), \( m\angle L = 33^\circ \)