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We see that two sides in a triangle are congruent. According to the base angles theorem the angles opposite these sides are congruent. Thus, by the theorem $∠A$ $≅$ $∠C.$ Therefore, these two angles have the same measure.

As a result, we have that $m∠A=48_{∘}.$

b

The following triangle is given.

As we can see from the figure, $m∠A≅m∠C.$ Therefore, we can immediately identify the measure of $∠A$ as $65_{∘}.$