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.