Question

△jkl≅△mnp.m∠l=(x² + 10)°, and m∠p=(2x² + 1)°. what is m∠l?

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle JKL\cong\triangle MNP\), then \(\angle L\cong\angle P\). So \(m\angle L = m\angle P\). Given \(m\angle L=(x^{2}+ 10)^{\circ}\) and \(m\angle P=(2x^{2}+1)^{\circ}\), we set up the equation \(x^{2}+10 = 2x^{2}+1\).

Step2: Solve the equation for \(x^{2}\)

Subtract \(x^{2}\) from both sides: \(10=x^{2}+1\). Then subtract \(1\) from both sides: \(x^{2}=9\).

Step3: Find \(m\angle L\)

Substitute \(x^{2}=9\) into the formula for \(m\angle L\). \(m\angle L=(x^{2}+10)^{\circ}=(9 + 10)^{\circ}=19^{\circ}\).

Answer:

\(19^{\circ}\)