Question

9 in the figure, the lines are parallel. what is the relationship given? supplementary vertical acute angle: ____ obtuse angle ____

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary. So, \(4x + 6+(- 5 + 5x)=180\).

Step2: Simplify the equation

Combine like - terms: \((4x+5x)+(6 - 5)=180\), which gives \(9x+1 = 180\).

Step3: Solve for \(x\)

Subtract \(1\) from both sides: \(9x=180 - 1=179\), then \(x=\frac{179}{9}\approx19.89\).

Step4: Calculate the angles

For the first angle: \(4x + 6=4\times\frac{179}{9}+6=\frac{716}{9}+\frac{54}{9}=\frac{716 + 54}{9}=\frac{770}{9}\approx85.56^{\circ}\) (acute angle).
For the second angle: \(-5 + 5x=-5+5\times\frac{179}{9}=-5+\frac{895}{9}=\frac{-45 + 895}{9}=\frac{850}{9}\approx94.44^{\circ}\) (obtuse angle).

Answer:

Acute Angle: \(\frac{770}{9}\approx85.56^{\circ}\), Obtuse Angle: \(\frac{850}{9}\approx94.44^{\circ}\)