Question

given that the top and bottom sides are parallel, find the value of x. then find the measure of each labeled angle. (x^{circ}=105^{circ}) ((x - 30)^{circ}=square^{circ})

Explanation:

Step1: Use property of parallel - sided figure

Since the top and bottom sides are parallel, the sum of the two adjacent angles is 180°. So we have the equation \(x+(x - 30)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+x-30 = 180\), which simplifies to \(2x-30=180\).

Step3: Solve for x

Add 30 to both sides of the equation: \(2x=180 + 30\), so \(2x=210\). Then divide both sides by 2: \(x=\frac{210}{2}=105\).

Step4: Find the measure of \((x - 30)^{\circ}\)

Substitute \(x = 105\) into \((x - 30)\): \(105-30=75\).

Answer:

\(x = 105\), \((x - 30)^{\circ}=75^{\circ}\)