Question

find the value of x using the figure, shown to the right. the value of x is (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify angle - relationship

The two angles \(3(x + 2)^{\circ}\) and \(81^{\circ}\) are corresponding angles (assuming the parallel - line setup indicated by the arrow marks on the lines). Corresponding angles are equal when two parallel lines are cut by a transversal. So we set up the equation \(3(x + 2)=81\).

Step2: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(3x+6 = 81\).

Step3: Isolate the variable term

Subtract 6 from both sides of the equation: \(3x+6−6=81 - 6\), which simplifies to \(3x=75\).

Step4: Solve for x

Divide both sides of the equation by 3: \(\frac{3x}{3}=\frac{75}{3}\), so \(x = 25\).

Answer:

25