SOLUTION: anglel and m are complementary. Angle p and N are complementary. angle l= y-2. m=2x+3 p=x-1 N=2x-y find x and y and the measure of each angle

Question 52644This question is from textbook Geometry
: anglel and m are complementary. Angle p and N are complementary. angle l= y-2. m=2x+3 p=x-1 N=2x-y find x and y and the measure of each angle This question is from textbook Geometry

Answer by gsmani_iyer(201) (Show Source): You can put this solution on YOUR website!

Angles l+m = 90 and n+p = 90 degrees. i.e.

angles l + m + n + p = 180 degrees

y-2+2x+3+x-1+2x-y = 180 degrees.

5x = 180 degrees. So x = 36.

angles l + m = y-2+2x+3 = 90 degrees.

2x + y + 1 = 90; so, 2x+y = 89; By replacing the value of x above, we get

2(36)+y = 89; i.e. 72 + y = 89.

y = 89-72 = 17.

x = 36; y = 17. Answer. The problem can be solved in a different way too.

y-2+2x+3 = 90 i.e. 2x+y+1 = 90; 2x+y = 89 .....(1)
x-1+2x-y = 90 i.e. 3x-y-1 = 90; 3x-y = 91 .....(2)
(2) + (1), we get 5x = 180; so x = 36. Now replacing this value of x in (1),
72+y = 89; So y = 17.
x = 36; y = 17. Answer. I think this helps you a lot.

gsm

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