SOLUTION: The second angle in a triangle is twice as large as the first. The third angle is three-fourths as large as the first. Find the angle measures and draw a possible picture

Algebra ->  Triangles -> SOLUTION: The second angle in a triangle is twice as large as the first. The third angle is three-fourths as large as the first. Find the angle measures and draw a possible picture      Log On


   

Question 698211: The second angle in a triangle is twice as large as the first. The third angle is three-fourths as large as the first. Find the angle measures and draw a possible picture
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The second angle beta in a triangle is twice as large as the first angle alpha:
beta=2alpha
The third angle gamma is three-fourths as large as the first angle alpha:
gamma=%283%2F4%29alpha
we know that alpha%2Bbeta%2Bgamma=180...substitute
beta=2alpha and gamma=%283%2F4%29alpha

alpha%2B2alpha%2B%283%2F4%29alpha=180....solve for alpha

3alpha%2B%283%2F4%29alpha=180

%283%2B3%2F4%29alpha=180
%2812%2F4%2B3%2F4%29alpha=180
%2815%2F4%29alpha=180
alpha=180%2F%2815%2F4%29
alpha=%28180%2A4%29%2F15
alpha=720%2F15
highlight%28alpha=48%29

now find beta=2alpha

beta=2%2A48
highlight%28beta=96%29

gamma=%283%2F4%29alpha
gamma=%283%2F4%2948
gamma=%283%2Fcross%284%29%29cross%2848%2912
gamma=3%2A12
highlight%28gamma=36%29

check:

alpha%2B2alpha%2B%283%2F4%29alpha=180
48%2B96%2B36=180
180=180