geometry question

Question

what are the possible values of <1 if <1=(x²+4x) <2=(x-162

Answer 1

if angles 1 and 2 are supplementary, then

x^2+4x + x-162 = 180

x^2 +5x - 342 = 0

use the quadratic formula if you can't factor

x= -2.5 +/- .5sqr(25+1368)

x = -2,5 +.5sqr1393

x = about -2.5 +37.32/2= -2.5+18.66

x = about 16.2

angle 2 = 16.2-162 = -145.8 degrees

angle 1 = 16.2^2 +4(16.2)= about 262.4 + 64.8 = 327.2 degrees

which should sum to 180, but there's an error somewhere above, in the arithmetic

close though, so it might just be rounding errors

if the two angles are complementary then

x^2 +4x + x -162 = 90

x^2 +5x - 72 = 0

use the quadratic formula

x =-2.5 +.5sqr(25+288)

= -2,5 + .5sqr313

= about 6.35

angle 1 = about 6.35^2 +4(6.345) =65.7 degrees

angle 2 = about 6.35 - 162 = -155.7 degrees

which sum to 90

possibly there's a misprint in the problem or it was miscopied

as this type of problem usually involves positive angles only