SOLUTION: Please help me understand the following: Three adjacent angles form a 90 degree angle. The second angle is twice the first angle and the third angle is 10 less than the sum of

Algebra ->  Angles -> SOLUTION: Please help me understand the following: Three adjacent angles form a 90 degree angle. The second angle is twice the first angle and the third angle is 10 less than the sum of       Log On


   

Question 384418: Please help me understand the following:
Three adjacent angles form a 90 degree angle. The second angle is twice the first angle and the third angle is 10 less than the sum of the other two angles. What is the measure of each angle?
Found 2 solutions by ewatrrr, stanbon:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,         

Let x, 2x and (3x - 10) represent the angles.

Question states:

x + 2x + (3x-10) = 90°

   6x - 10 = 90°

       6x = 100°

        x = 100°/6 = 50/3 = 16 2/3 °  

   16 2/3 ° 1s the  measure of the first angle

   33 1/3 ° 1s the  measure of the second angle 

     40 ° 1s the  measure of the third angle



CHECKING our Answer

 16 2/3 ° + 33 1/3 ° + 40° = 50° + 40° = 90°

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Three adjacent angles form a 90 degree angle. The second angle is twice the first angle and the third angle is 10 less than the sum of the other two angles. What is the measure of each angle?
----
x + y + z = 90
y = 2x
z = (x+y)-10
-----------------
Rearrange:
x + y + z = 90
2x - y + 0 = 0
x + y - z = 10
-----------------------
Solve by any method you know to get:
x = 16 2/3 degrees
y = 33 1/3 degrees
z = 40 degrees
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Cheers,
Stan H.