Question

14 given ( mangle lnk=(7x + 2)^{circ} ) and ( mangle knp=(10x + 3)^{circ} ), solve for x.

Explanation:

Step1: Use the property of complementary angles

Since \(\angle LNK\) and \(\angle KNP\) are complementary (they form a right - angle), we have the equation \(m\angle LNK+m\angle KNP = 90^{\circ}\).
Substitute \(m\angle LNK=(7x + 2)^{\circ}\) and \(m\angle KNP=(10x+3)^{\circ}\) into the equation: \((7x + 2)+(10x + 3)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(7x+10x+2 + 3=90\), which simplifies to \(17x+5 = 90\).

Step3: Isolate the variable \(x\)

Subtract \(5\) from both sides of the equation: \(17x+5-5=90 - 5\), so \(17x=85\).
Divide both sides by \(17\): \(x=\frac{85}{17}\).

Answer:

\(x = 5\)