SOLUTION: help me figure out proofs involving triangles? Given: m∠3 = m∠7 m∠2 = 60° m∠6 = 115° m∠5 = ? I've figured out that m∠4 = 10, but from

Algebra ->  Geometry-proofs -> SOLUTION: help me figure out proofs involving triangles? Given: m∠3 = m∠7 m∠2 = 60° m∠6 = 115° m∠5 = ? I've figured out that m∠4 = 10, but from       Log On


   

Question 554559: help me figure out proofs involving triangles?
Given: m∠3 = m∠7
m∠2 = 60°
m∠6 = 115°
m∠5 = ?
I've figured out that m∠4 = 10, but from there how would i figure out what m∠5 equals? Here's a pic of the triangle below

http://assets.openstudy.com/updates/attachments/4f0b3b0be4b014c09e64bd2b-avieira-1326136086980-page69b.gif
Thank you so much in advance!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
help me figure out proofs involving triangles?
Given: m∠3 = m∠7
m∠2 = 60°
m∠6 = 115°


Since m∠2 = 60°, m∠1 = 180°-60° = 120°

Since m∠6 = 115°, m∠5 = 180°-115° = 65°

That's all you wanted, but I'm going to find them all, since
no doubt you'll need to know how.

Since m∠5 = 65° and m∠2 = 60°, and angles 2,3, and 5 are interior angles
of the same triangle, and have sum 180°, then m∠3 = 180°-65°-60° = 55°

m∠7 = 55°, since we are given that m∠3 = m∠7

Since m∠6 = 115° and m∠7 = 55°, and angles 4,6, and 7 are interior angles
of the same triangle, and have sum 180°, then m∠4 = 180°-115°-55° = 10°
(You got that one right, but you didn't need it to find m∠5)

m∠1 = 120°
m∠2 = 60°
m∠3 = 55°
m∠4 = 10°
m∠5 = 65°
m∠6 = 115°
m∠7 = 55°

Edwin