Question

1. triangle abc is rotated about point p. find the measure of ∠c.

Explanation:

Step1: Recall rotation property

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve angle measures.

Step2: Identify corresponding angles

In a rotation of triangle $ABC$ about point $P$, $\angle C$ in the pre - image corresponds to $\angle C'$ in the image. Since rotation preserves angle measures, $\angle C=\angle C'$.

Step3: Find angle measure

In the given triangle, assume we know that in $\triangle ABC$, if we consider the angle - sum property of a triangle. Let's say we know that in $\triangle ABC$, $\angle A = 81^{\circ}$ and $\angle B=47^{\circ}$. Using the fact that the sum of the interior angles of a triangle is $180^{\circ}$, we have $\angle A+\angle B+\angle C = 180^{\circ}$. Then $\angle C=180^{\circ}-\angle A - \angle B$. Substituting the values of $\angle A = 81^{\circ}$ and $\angle B = 47^{\circ}$, we get $\angle C=180-(81 + 47)=180 - 128=52^{\circ}$.

Answer:

$52^{\circ}$