Answer:
8 units
Step-by-step explanation:
» Concepts
Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.
» Application
In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.
» Solving
Step 1: Subtract q from both sides.
- [tex]4q-8-q=q+4-q[/tex]
- [tex]3q-8=4[/tex]
Step 2: Add 8 to both sides.
- [tex]3q-8+8=4+8[/tex]
- [tex]3q=12[/tex]
Step 3: Divide both sides by 3.
- [tex]3q/3 = 12/3[/tex]
- [tex]q=4[/tex]
Step 4: Plug in the value of q for side AB.
- [tex]4(4)-8[/tex]
- [tex]16-8[/tex]
- [tex]8[/tex]
Therefore, the answer is 8 units.
