Question

1. in \\( \triangle jkl \\), if \\( m\angle k \\) is nine more than \\( m\angle l \\), and \\( m\angle j \\) is 21 less than twice \\( m\angle l \\), find the measure of each angle.\\( m\angle j = \underline{\quad}\\)\\( m\angle k = \underline{\quad}\\)\\( m\angle l = \underline{\quad}\\)

Explanation:

Step1: Define variables

Let \( m\angle L = x \). Then \( m\angle K = x + 9 \), and \( m\angle J = 2x - 21 \).

Step2: Use triangle angle sum

In \( \triangle JKL \), \( m\angle J + m\angle K + m\angle L = 180^\circ \). Substitute: \( (2x - 21)+(x + 9)+x = 180 \).

Step3: Simplify equation

Combine like terms: \( 2x - 21 + x + 9 + x = 180 \) → \( 4x - 12 = 180 \).

Step4: Solve for x

Add 12: \( 4x = 192 \) → \( x = 48 \).

Step5: Find each angle

• \( m\angle L = x = 48^\circ \)
• \( m\angle K = x + 9 = 57^\circ \)
• \( m\angle J = 2x - 21 = 2(48)-21 = 75^\circ \)

Answer:

\( m\angle J = 75^\circ \), \( m\angle K = 57^\circ \), \( m\angle L = 48^\circ \)