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Consider the given diagram.

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

Next, we know by the interior angles theorem that the sum of the measures of the interior angles of a triangle equals $180_{∘}.$

$m∠A+m∠B+m∠C=180 $ Applying the theorem, we can write an equation in terms of $x.$ $x+x+50=180$ Let's solve the equation for $x.$ b

Consider the given diagram. Note that $AB$ $≅$ $BC$ and therefore $△ABC$ is an isosceles triangle. The triangle's vertex angle, $∠ABC,$ is bisected by $BO.$

For the triangle $ABC$ we can apply the base angles theorem. Thus, $∠A≅∠C$ and they must have the same measure.

Next, we apply use the interior angles theorem on $△ABC.$