Question

1. in $\triangle jkl$, if $m\angle k$ is nine more than $m\angle j$ and $m\angle l$ is 21 less than twice $m\angle j$, find the measure of each angle.

$m\angle k = x + 9$
$m\angle j = x$
$m\angle l = 2x - 21$
\hfill $= 180^\circ$
$m\angle j = \underline{\quad\quad}$
$m\angle k = \underline{\quad\quad}$
$m\angle l = \underline{\quad\quad}$

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(m\angle J + m\angle K + m\angle L = 180^\circ\).
Substitute \(m\angle J = x\), \(m\angle K = x + 9\), \(m\angle L = 2x - 21\) into the equation:
\(x + (x + 9) + (2x - 21) = 180\)

Step2: Simplify and solve for \(x\)

Combine like terms:
\(x + x + 9 + 2x - 21 = 180\)
\(4x - 12 = 180\)
Add 12 to both sides:
\(4x = 180 + 12\)
\(4x = 192\)
Divide both sides by 4:
\(x = \frac{192}{4} = 48\)

Step3: Find each angle

• \(m\angle J = x = 48^\circ\)
• \(m\angle K = x + 9 = 48 + 9 = 57^\circ\)
• \(m\angle L = 2x - 21 = 2(48) - 21 = 96 - 21 = 75^\circ\)

Answer:

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