Question

△ABC is similar to △XYZ. Also, angle A measures 45° and angle C measures 60°.


What is the measure of angle Y?



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Answer 1

in any triangle all angles must equal 180 so if A is 45 (half right angle) and C is 60 then add them to get 105 then minus it from 180 to get 75 the answer for B

ABC triangle is the same amount as XYZ  A and X the fist letters are 45 C and Z are 60 and and B and Y are 75

Answer 2

Applying the sum of triangle theorem and similarity theorem, the measure of angle Y is: 75°

Recall:

The corresponding angles of two triangles that are similar are always congruent, meaning they are equal in measure.

Thus, given that △ABC is similar to △XYZ, where:

• ∠A = 45°
• ∠C = 60°

Note:

• ∠A ≅ ∠X

• ∠B ≅ ∠Y

• ∠C ≅ ∠Z

• Since ∠B ≅ ∠Y, therefore,

m∠B = m∠Y = 180° - (45° + 60°) (sum of triangle)

m∠Y = 180° - 105°

m∠Y = 75°

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