Question

4 given the diagram below, where lines a and b are parallel, which of the following statements are true? select all that apply
a. the angles with measures 25x + 80 and 48 + x are supplementary.
b. 25x + 80 = 48 + x.
c. each of the acute angles in the diagram has a measure of 2 degrees.
d. each of the obtuse angles in the diagram measures 130 degrees.

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((25x + 80)+(48 + x)=180\).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Step3: Find the measure of angles

Substitute \(x = 2\) into \(25x+80\): \(25\times2+80=50 + 80=130\)
Substitute \(x = 2\) into \(48+x\): \(48+2=50\)

The acute angles (non - supplementary to \(130^{\circ}\) angles) have a measure of \(50^{\circ}\), and the obtuse angles have a measure of \(130^{\circ}\)

Answer:

A. The angles with measures \(25x + 80\) and \(48 + x\) are supplementary.
D. Each of the obtuse angles in the diagram measures \(130\) degrees.