Expert: Bobby Soltani - 7/5/2005

Question
1.Two complimentary angles are such that one is 10 degress less than 3 times the other.Find the angles.
2.The base angles in an isosceles triangle are both 25 degress less than twice the third angle. Find the measures of all three angles?

Answer
Hi Clemente,

1) let one angle be "a" and the other be "b".  We know from the definition of complementary angles that a + b = 90.  Also, we are given that one is 10 less than 3 times the other.  We can write this in equation form as
a = 3b - 10

Now, we have two equations and two unknowns.  Solve the first equation for b.
a + b = 90
subtract a from both sides
b = 90 - a
plug in this value for b into the second equation
a = 3(90 - a) - 10
solve for a
a = 270 - 3a - 10
4a = 260
a = 65 degrees
now using the first equation, we can get b
b = 90 - a
b = 90 - 65
b = 25 degrees

2) we have three angles: a, b, and c.  From the definition of an isosceles triangle, we know that a = b.  From the problem, we are given that
a = 2c - 25
and
b = 2c - 25
Also, the sum of all the angles in a triangle is equal to 180 degrees.  So, we can write
a + b + c = 180
since b = a,
a + a + c = 180
2a + c = 180
We can use this last equation and a = 2c - 25 to solve for a and c.
from the first equation, c = 180 - 2a.  Plugging that in for c in the second equation, we get
a = 2(180 - 2a) - 25
a = 360 - 4a - 25
5a = 335
a = 67
we know that b = a, so b = 67 degrees
we know that a + b + c = 180, so c = 180 - 67 - 67 = 46 degrees.

Let me know if you have any questions.

Bobby