Question

solve for x.
x = 144
x = 54
x = 9
x = 24

Explanation:

Step1: Use the property of right - angled triangles

In a right - angled triangle, the sum of the two non - right angles is \(90^{\circ}\). Here, one non - right angle is \(20^{\circ}\), and the other non - right angle is related to the expression \(6x + 16\). So, \(6x+16 + 20=90\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(6x+36 = 90\).

Step3: Isolate the term with \(x\)

Subtract \(36\) from both sides of the equation: \(6x=90 - 36\), so \(6x = 54\).

Step4: Solve for \(x\)

Divide both sides of the equation by \(6\): \(x=\frac{54}{6}\).

Answer:

\(x = 9\)