Suppose EP =PG. Explain how you can find m

Question

Suppose EP =PG. Explain how you can find m<PQG

mathstudent55 · Answer

Picture?

anonymous · Answer

Here is the picture

mathstudent55 · Answer

|dw:1355898270720:dw|

mathstudent55 · Answer

Your pic is very dark. Does this look like it? I just added little marks to show EP = PG from your given.

anonymous · Answer

Yes

mathstudent55 · Answer

One way of proving two triangles are similar is to show that for two sides and the included angle of the two triangles, the lengths of the corresponding sides are proportionals and the included angles are congruent.

mathstudent55 · Answer

Do you understand the above statement on how to prove two triangles similar?

anonymous · Answer

I am a bit confused on the explanation

mathstudent55 · Answer

Do you know the regular SAS to prove triangles are congruent?

anonymous · Answer

Not real well

mathstudent55 · Answer

Ok, look at the following picture.

mathstudent55 · Answer

|dw:1355899027318:dw|

anonymous · Answer

okay

mathstudent55 · Answer

Look at the two triangles. The one on the left has a side measuring 6, one side measuring 7 and the included angle (the angle between those sides) measuring 50.

anonymous · Answer

okay

mathstudent55 · Answer

The one on the right has one side measuring 12, one side measuring 14, and the included angle (the angle between those sides) measuring 50.

anonymous · Answer

yeah

mathstudent55 · Answer

Notice that the included angles of the two triangles are congruent. They both measure the same.

anonymous · Answer

yes

mathstudent55 · Answer

Also notice that the lengths of the corresponding sides 6 corresponds to 12, and 7 corresponds to 14, are in the same proportion. If you multiply 6 by 2 you get 12, and if you multiply 7 by 2 (again 2) you get 14.

mathstudent55 · Answer

This means the triangles are similar.

anonymous · Answer

ohhhh I get it! Thank you :)

anonymous · Answer

Makes sense

mathstudent55 · Answer

Now you need to prove the two triangles of your problem are similar. They are similar, you just need to prove it. Then, since <PQG corresponds to <F, they congruent, so <PQG measures 85.

anonymous · Answer

Okay so the answer would be <PQG 85

agent0smith · Answer

Correct @missylove 

heh, i originally misread the question as asking you to find <PGQ, which is impossible from the given angles/sides. @mathstudent55 's answer was the point I realized I'd read the question wrong.