SOLUTION: The sum of the measures of the angles of any quadrilateral is 360°. The measures of ∠A and ∠B are the same. The measure of ∠C is 17° greater than the measure of &

Algebra ->  Polygons -> SOLUTION: The sum of the measures of the angles of any quadrilateral is 360°. The measures of ∠A and ∠B are the same. The measure of ∠C is 17° greater than the measure of &      Log On


   

Question 977524: The sum of the measures of the angles of any quadrilateral is 360°. The measures of ∠A and ∠B are the same. The measure of ∠C is 17° greater than the measure of ∠A, and the measure of ∠D is 37° less than ∠B. Find the measure of ∠A, ∠B, ∠C, and ∠D.
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28A=B%2CC=17%2BA%2CD=-37%2BB%2CA%2BB%2BC%2BD=180%29

That is the system. Do you need more help?
-Yes!-

Try to use the first equation to eliminate A.
system%28C=B%2B17%2CD=B-37%2CB%2BB%2BC%2BD=360%29
-
system%28C=B%2B17%2CD=B-37%2C2B%2BC%2BD=360%29,
and notice how two of these equations are in terms of just B...
substitute for them in the "360" equation:
highlight_green%282B%2B%28B%2B17%29%2B%28B-37%29=360%29
Work with this to solve for the value of B.
Do what you know you need to finish.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Solve for then calculate and

John

My calculator said it, I believe it, that settles it