Question

Triangle ABC is similar to triangle XYZ by the AA Similarity Postulate. Also, m∠A = 44° and m∠C = 31°. What is m∠Y

Answer 1

m∠Y = 105 degrees

Step by step explanation

Here ΔABC and ΔXYZ are similar. Therefore, the angles of the two triangles are equal in measure.

m∠A = 44 = m∠X, m∠C = 31 = m∠Z

m∠Y = m∠B

m∠X + m∠Y +m∠Z = 180 {sum of the interior angles add upto 180]

44 + m∠Y + 31 = 180

75 + m∠Y = 180

m∠Y = 180 - 75

m∠Y = 105

Thank you.

Answer 2

Y = 105°

Explanation:

We know that triangle ABC is similar to triangle XYZ by the AA similarity postulate.

According to the AA similarity postulate, if two triangles are similar then all the corresponding angle pairs are congruent and all corresponding sides are proportional.

So it means that angles ABC are congruent to angles XYZ, in this case.

If m∠A = 44° and m∠C = 31°, then B = 180 - (44 + 31) = 105°.

Therefore, angle Y = 105° as it is the corresponding angle to B.