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F. Correct. The measures of angles in a triangle sum to 180°, so in △ABC, $m\angle A+m\angle B+m\angle C=180°$. Since $\angle A\cong \angle C$, $m\angle A=m\angle C$. Substituting this relationship and $m\angle B=143.6°$ into the initial equation yields $m\angle A+143.6°+m\angle A=180°$. Subtract 143.6° from each side of the equation and divide each side by 2 to calculate $m\angle A=\left(\frac{180-143.6}{2}\right)°=18.2°$.

G. Incorrect. You may have started correctly by subtracting $m\angle B=143.6°$ from $180°$. Then, remember that the difference, 36.4°, is twice the measure of the desired angle since the remaining two angles are congruent. Try dividing your answer by 2.

H. Incorrect. You may have thought that $m\angle A+m\angle C=143.6°$ so that $2\left(m\angle A\right)=143.6°\leftrightarrow m\angle A=71.8°$. Remember that the given angle measure is $m\angle B$, not $m\angle A+m\angle C$.

J. Incorrect. You may have thought that $m\angle A=m\angle B$. Be sure to carefully read the given information.