FIRST QUESTION: if triangle XYZ is similar to triangle PMN, what is the value of ∠X when ∠P=30°?

Question

FIRST QUESTION: if triangle XYZ is similar to triangle PMN, what is the value of ∠X when ∠P=30°?

SECOND QUESTION: if triangle XYZ is similar to triangle PMN and side X=6, side Y=2, and side P=12, what is the length of side M?

Answer 1

First Question: The corresponding angles of similar triangles are equal. <X and <P are corresponding angles so they are equal and <X = <P = 30.

Second Question: The ratio of corresponding sides of similar triangles are the same. So the ratio of X to P will equal the ratio of Y to M:

6 = 2

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12 M

M = 4