Two angles are vertical angles. One angle is labeled 2x degree. The other angle is labeled (x + 30) degrees. Find the value of x.

(a) C

(b) E

Step-by-step explanation:

aₙ = xⁿ / n!

aₙ₊₁ = xⁿ⁺¹ / (n+1)!

lim(n→∞)│aₙ₊₁ / aₙ│

lim(n→∞)│[xⁿ⁺¹ / (n+1)!] / [xⁿ / n!]│

lim(n→∞)│[xⁿ⁺¹ / (n+1)!] × [n! / xⁿ]│

lim(n→∞)│[xⁿ⁺¹ / xⁿ] × [n! / (n+1)!]│

lim(n→∞)│x / (n+1)│

x is a constant, so the limit equals 0 for all values of x.  The limit is always less than 1, so the series is convergent.