Triangle $A B C$ is translated 5 units to the right and 4 units up to create triangle $A^{\prime} B^{\prime} C^{2}$.

What is the measure of $\angle B$ ?

Question

Triangle $A B C$ is translated 5 units to the right and 4 units up to create triangle $A^{\prime} B^{\prime} C^{2}$.

What is the measure of $\angle B$ ?

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the given information from the problem and the image. ‖ ‖ step 2 ⋮ Recognize that a translation does not change the angles of a triangle. ‖ ‖ step 3 ⋮ Use the fact that the sum of angles in a triangle is $180^\circ$ to find the measure of $\angle B$. ‖ ‖ step 4 ⋮ Calculate the measure of $\angle B$ by subtracting the measures of $\angle A$ and $\angle C$ from $180^\circ$. ‖ ‖ step 5 ⋮ $\angle B = 180^\circ - \angle A - \angle C = 180^\circ - 80^\circ - 26^\circ$. ‖ ‖ step 6 ⋮ Perform the subtraction to find the measure of $\angle B$. ‖ ‖ step 7 ⋮ $\angle B = 180^\circ - 80^\circ - 26^\circ = 74^\circ$. ‖ ∻Answer∻ ⚹ The measure of $\angle B$ in triangle ABC is $74^\circ$. ⚹ ∻Key Concept∻ ⚹Sum of Angles in a Triangle⚹ ∻Explanation∻ ⚹The sum of the interior angles of any triangle is always $180^\circ$. By knowing two angles, we can find the third◊What is the relationship between the angles of two similar triangles when one is translated or rotated to create the other?⍭ Generate me a similar question◊⚹

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