angle 1 angle 2 angle 3 are adjacent. With angle 1 supplementary to angle 2 and angle 2 complementary to angle 3. If angl118x+3 and angle2=5x-18, what is angle3

Question

heeelppp meee

Answer 1

I will use the following convention

Angle1 = m1

Angle2 = m2

Angle3 = m3

 

Given:

m1 + m2 = 180  (Supplementary angles) ---------------------------------(1)

m2 + m3 = 90    (Complementary angles) --------------------------------(2)

m1 = 18x + 3      ------------------------------------------------------------(3)

m2 = 5x - 18       ------------------------------------------------------------(4)

 

using (1) we can write,

m2 = 180 - m1   -------------------------------------------------------------(5)

substituting (5) in (2)

180 - m1 + m3 =90  ---------------------------------------------------------(6)

now substituting (3) in (6)

m3 = 18x - 87 ----------------------------------------------------------------(7)

 

To find x add (3) and  (4) and equate to (1)

180 = 23x - 15

x = 180/ 23 -------------------------------------------------------------------(8)

 

Now using (8) in (7)

 

m3 = 53.86

or

m3 ~ 54