Question

6
(12x + 1)°
k
3x°
(16x - 7)°
j
l
m∠j = ___°
m∠k = ___°
m∠l = ___°

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(3x+(12x + 1)+(16x-7)=180\).

Step2: Combine like - terms

\((3x+12x + 16x)+(1 - 7)=180\), which simplifies to \(31x-6 = 180\).

Step3: Solve for x

Add 6 to both sides: \(31x=180 + 6=186\). Then divide both sides by 31: \(x=\frac{186}{31}=6\).

Step4: Find the measure of each angle

For \(\angle J\): Substitute \(x = 6\) into \(m\angle J=3x\), so \(m\angle J=3\times6 = 18^{\circ}\).
For \(\angle K\): Substitute \(x = 6\) into \(m\angle K=12x + 1\), so \(m\angle K=12\times6+1=72 + 1=73^{\circ}\).
For \(\angle L\): Substitute \(x = 6\) into \(m\angle L=16x-7\), so \(m\angle L=16\times6-7=96-7 = 89^{\circ}\).

Answer:

\(m\angle J = 18^{\circ}\)
\(m\angle K = 73^{\circ}\)
\(m\angle L = 89^{\circ}\)