Answer:
The value of x is 4, and the measure of the four angles are 100°, 80°, 100°, 80°.
Step-by-step explanation:
There is a rule that states the following: when two lines intersect, the verticle/opposite angles formed will have the same degree measure. Using this rule, we can infer that [tex]30x-20=10x+60[/tex]. To solve for x, isolate the variable all on one side of the equation. [tex]30x-10x = 60 + 20[/tex] ⇒ [tex]20x = 80[/tex] ⇒ [tex]x=4[/tex]. Since we now know the value of x, you can use that to figure out a pair of verticle angles, apply the value of x to any equation and you'll get that two of the four angles are all 100°. Since the rotation of a full circle is 360°, you can get that the sum of the remaining two angles is 360° - 100° * 2 = 360° - 200° = 160°. Because we know the remaining pair of verticle angles are equal, we can get that each of the remaining angles is equal to [tex]\frac{160}{2}[/tex] or 80°, so the measure of all four angles are 100°, 80°, 100°, 80°.
