3. Use the following image to answer the questions. (a) How are the triangles similar? Justify your answer with a theorem or postulate. (b) What is the value of x? Show your work.? HELP

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1 Answer
Ananda Dasgupta
Feb 13, 2018

#x=5#

Explanation:

It is given that #/_ ABC = /_PQR # and #/_CAB = /_RPQ# . Since the sum of the three angles of both triangles must be 180 degrees, we have #/_BCA = /_ QRP# . Since all three angles of the two triangles are equal, they are similar.

Since sides opposite to identical angles are proportional for similar triangles, we have
#{3x+6}/24 = 28/32 implies 3x+6 = 28/32\times 24 = 21# #

implies 3x = 15 implies x=5#

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