Right triangle ABC is similar to triangle XYZ because angle B is congruent to angle Y. If angle C equals 27°,what is the measure of angle Z?
Your subject is math.
27 degres
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To find the measure of angle Z, we need to use the fact that similar triangles have corresponding angles that are congruent.
Since triangle ABC is similar to triangle XYZ, we know that angle B is congruent to angle Y.
Given that angle C equals 27°, we can use the fact that the sum of the angles in a triangle is always 180° to find the measure of angle A.
First, we can find the measure of angle A using the equation:
angle A + angle B + angle C = 180°
Substituting the known values:
A + B + 27 = 180
Since angle B is congruent to angle Y, we can substitute angle Y for angle B:
A + Y + 27 = 180
Rearranging the equation:
A + Y = 180 - 27
A + Y = 153
Now, we can use the fact that corresponding angles of similar triangles are congruent to find the measure of angle Z.
Since angle B is congruent to angle Y, we can substitute angle B for angle Y in the equation:
A + B = 153
Since triangle ABC is similar to triangle XYZ, we can say:
angle A + angle B + angle C in triangle XYZ = A + B + 27 in triangle ABC.
Therefore, angle Z + angle Y + 27 = A + B + 27
angle Z + Y + 27 = 153
Substituting angle Y with angle B:
angle Z + B + 27 = 153
Simplifying the equation:
angle Z + B = 153 - 27
angle Z + B = 126
Now, we can substitute the value of angle B (which is congruent to angle Y and equal to angle B) into the equation:
angle Z + angle B = 126
angle Z + B = 126
Since angle B is congruent to angle Y, we can rewrite the equation as:
angle Z + angle Y = 126
Since corresponding angles of similar triangles are congruent, we can conclude that angle Z is also equal to 126°.