Question

11 using the diagram below, solve for x. (6x + 25)° (2x + 3)°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The sum of \((2x + 3)^{\circ}\) and \((6x + 25)^{\circ}\) is \(90^{\circ}\) (since they are complementary to the right - angle). So, \(2x+3 + 6x + 25=90\).

Step2: Simplify the equation

Combine like terms: \(8x+28 = 90\).

Step3: Solve for \(x\)

Subtract \(28\) from both sides: \(8x=90 - 28\), \(8x = 62\). Then divide both sides by \(8\): \(x=\frac{62}{8}=\frac{31}{4}=7.75\).

Answer:

\(7.75\)