Geometry Question Help

Question

The measures of the angles of a triangle are:
m<A = 2√2x degrees
m<B = 5√2x degrees
m<C = 2√2x degrees

Find measures of the angles and classify

Answer 1

2√2x+5√2x+2√2x=180

9√2x=180

√2x=20

2*20=40º

5*20=100º

2*20=40º

note: we could have squared both sides of √2x=20 to get 2x=400 and x=200; then we would have had √400=20 again but this is not necessary

obtuse isosceles triangle with base angles of 40º each

Answer 2

The three angles add up to 180^o.  So add them up and set them equal to 180:

 

     2√(2x + 5 √(2x) + 2√(2x) = 180

     9√(2x) = 180

     √(2x) = 20

     2x = 20²

     2x = 400

     x = 200

 

To find angles A, B and C.  Plug x=200 into the equations for each angle.  Check by making sure they add up to 180^o.