Question

solve for x. (image: right triangle with one angle 20°, another angle labeled (6x + 16), and a right angle marked with a red square.)

Explanation:

Step1: Recall triangle angle sum

In a right triangle, the two non - right angles sum to \(90^{\circ}\). So we have the equation \(20^{\circ}+(6x + 16)^{\circ}=90^{\circ}\).

Step2: Simplify the equation

First, combine the constant terms: \(20 + 16+6x=90\), which simplifies to \(36 + 6x=90\).

Step3: Solve for x

Subtract 36 from both sides: \(6x=90 - 36\), so \(6x = 54\). Then divide both sides by 6: \(x=\frac{54}{6}=9\).

Answer:

\(x = 9\)