Question

practice describing supplementary angle relationships

• study the example showing how to use angle relationships to solve problems. then solve problems 1–8.

example
what is the value of x?
∠acd and ∠dfg are same - side exterior angles. ac and eg are parallel, so m∠acd + m∠dfg = 180°.
3x + 6x + 81 = 180
9x = 99
x = 11
(there is a diagram here showing two parallel lines cut by a transversal and another line, with angle expressions like (6x + 81)° and 3x°)
1 what is the angle relationship between ∠dcf and ∠cfg in the example? what are the measures of these angles? show your work.
vocabulary
same - side exterior angles
when two lines are cut by a transversal, a pair of angles on the same side of the transversal and outside the two lines.
same - side interior angles
when two lines are cut by a transversal, a pair of angles on the same side of the transversal and between the two lines.
transversal
a line that cuts two or more lines.
solution
2 find the value of x. show your work.
(there is a diagram here showing two parallel lines cut by a transversal, with angles (x - 50)° and x°)

Explanation:

Step1: Identify Angle Relationship

The two angles \((x - 50)^\circ\) and \(x^\circ\) are same - side exterior angles? No, wait, looking at the diagram (two parallel lines cut by a transversal? Wait, the two angles are adjacent? Wait, no, the two angles \((x - 50)^\circ\) and \(x^\circ\) are supplementary? Wait, no, actually, if we consider the straight line, the sum of angles on a straight line is \(180^\circ\)? Wait, no, the two angles \((x - 50)^\circ\) and \(x^\circ\) are same - side exterior? Wait, no, let's re - examine. The two angles \((x - 50)^\circ\) and \(x^\circ\) are supplementary? Wait, no, the correct relationship: since the two lines are parallel (the two non - horizontal lines) and the horizontal line is a transversal, the two angles \((x - 50)^\circ\) and \(x^\circ\) are same - side exterior angles? Wait, no, actually, the sum of same - side exterior angles when lines are parallel? Wait, no, let's think again. The two angles \((x - 50)^\circ\) and \(x^\circ\) are supplementary? Wait, no, the correct equation: since the two angles form a linear pair? Wait, no, the diagram shows two angles on a straight line? Wait, no, the two non - horizontal lines are parallel, and the horizontal line is a transversal. The two angles \((x - 50)^\circ\) and \(x^\circ\) are same - side exterior angles, and same - side exterior angles are supplementary when lines are parallel. So \((x - 50)+x = 180\).

Step2: Solve the Equation

$$
LATEXBLOCK0
$$

Answer:

The value of \(x\) is \(115\).