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Video: Using Properties of Congruence between Two Triangles

Bethani Gasparine

Given that △𝐴𝐵𝐶 ≅ △𝑋𝑌𝑍, find 𝑚∠𝐴.

02:03

Video Transcript

Given that triangle 𝐴𝐵𝐶 is congruent to triangle 𝑋𝑌𝑍, find the measure of angle 𝐴.

Since our triangles are congruent, that means their corresponding angles are also congruent which means they are equal in measure. Therefore, angle 𝐴 is congruent to angle 𝑋, angle 𝐵 is congruent to angle 𝑌, and angle 𝐶 is congruent to angle 𝑍.

Now we know that angle 𝑌 is equal to sixty-six degrees which means angle 𝐵 is sixty-six degrees. We also know what angles 𝑍 is equal to, which is equal to thirty-five degrees which means angle 𝐶 is equal to thirty-five degrees. And we don’t know angle 𝐴 or angle 𝑋. However, we do know that the sum of the measures of the angles on our triangle is equal to one hundred and eighty degrees. Therefore, the measure of angle 𝐴 plus the measure of angle 𝐵 plus the measure of Angle 𝐶 should be equal to one hundred and eighty degrees. Let’s go ahead and plug in sixty-six for angle 𝐵 and thirty-five for angle 𝐶.

Now when we’re solving, we can get rid of the degrees symbol but make sure that we attach it to our answer. So in order to solve for the measure of angle 𝐴, we need to add sixty-six and thirty-five together. So now we have the measure of angle 𝐴 plus one hundred and one equals one hundred and eighty. So to solve for the measure of angle 𝐴, we need to subtract one hundred and one from both sides of the equation. And one hundred and eighty minus one hundred and one is seventy-nine.

Therefore, the measure of angle 𝐴 is equal to seventy-nine degrees.