Question 551380: Find the angles of a triangle if one angle exceeds a second angle by 45 degrees and is three times as large as the third angle.
ASKER: I think this had been asked already but I badly wanted the explanation to be more clear like how they arrived with the answer. Thank you.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the 3 aqngles be x, y and z.
x is the measure of angle 1
y is the measure of angle 2
z is the measure of angle 3
since x is 45 degrees more than the measure of angle y, we have:
x = y + 45
since x is 3 times the measure of angle za, we have:
x = 3z
we know that the sum of the interior angles of a triangle is equal to 180 degrees.
this means that:
x + y + z = 180
if x is equal to y + 45, this means that y is equal to x - 45.
we can substitute for y to get:
x + x - 45 + z = 180
since x is equal to 3z, thismeans that z is equal to x/3.
we can substitute for z to get:
x + x - 45 + x/3 = 180
if we multiply both sides of this equation by 3,we will get:
3x + 3x - 3(45) + x = 3(180)
we simplify this and combine like terms to get:
7x - 135 = 540
we add 135 to both sides of this equation to get:
7x = 675
we divide both sides of this equation by 7 to get:
x = 675 / 7
let's see if that works.
angle 1 is equal to x which is equal to 675 / 7
angle 2 is equal to y which is equal to x - 45.
since 45 degrees is equal to 7*45/7 = 315 / 7, then angle 2 is equal to 675 / 7 minus 315 / 7 which makes it equal to 360 / 7.
angle 3 is equal to z which is equal to x/3.
this makes angle 3 equal to (675/7) * (1/3) which makes angle 3 equal to 225 / 7.
we have:
angle 1 = 675 / 7
angle 2 = 360 / 7
angle 3 = 225 / 7
add them all up together and you get 1260 / 7 which is equal to 180 degrees.
everything works out so the answer is that angle 1 is equal to 675 / 7 degrees.
in decimal form, this comes out to be 96.42857142857
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