SOLUTION: if the difference between the measures of two smaller angles of right triangle is 20 degrees, what is the measure , in degrees,of the smallest angle ?

Question 328008: if the difference between the measures of two smaller angles of right triangle is 20 degrees, what is the measure , in degrees,of the smallest angle ?
Found 2 solutions by mananth, jessica43:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
if on eangle = x
the other will be 90-x
..
x-90+x=20 (The sum of all angles of triangle = 180.one angle is x and the other 90. The third angle will be 90-x)
2x=110
x=55
the other angle will be 90-55=35
The angles are 55, 35
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
To solve this problem, you are going to need to write two equations using what you know.
First, you know that you have a right triangle. This means that one angle is 90 degrees, and the sum of the two smaller angles must equal 90 degrees (because the sum of the angles of a triangle is 180):
A + B + C = 180
90 + B + C = 180
B + C = 90 (where A is the right angle, B and C are the smaller angles)
Second, you know that the difference between the measures of the two smaller angles is 20 degrees:
B - C = 20 (where C is the smallest angle of the triangle)
This can be rewritten as B = 20 + C
Now plug in this second equation into the first equation and solve for C:
B + C = 90
(20 + C) + C = 90
20 + 2C = 90
2C = 70
C = 35
So the smallest angle is 35 degrees.
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