SOLUTION: In a triangle, the first angle measures 3 times the second and the third measures 20 degress less than the second. find each angle's measure.

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Question 204538This question is from textbook
: In a triangle, the first angle measures 3 times the second and the third measures 20 degress less than the second. find each angle's measure. This question is from textbook

Found 3 solutions by jojo14344, alicealc, nerdybill:
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We know the angles in a triangles add to 180 deg.

Let the Angles be system%28A=1st%2CB=2nd%2CC=3rd%29

It follows ---> A%2BB%2BC=180%5Eo, working eqn.

First condition:
The first angle measures 3 times the second: A=3B

Second condition:
The third measures 20 degrees less than the second: C=B-20%5Eo

Substituting to the working eqn,
highlight%283B%29%2BB%2Bhighlight%28B-20%5Eo%29=180%5Eo
5B=180%2B20=200%5Eo ---> cross%285%29B%2Fcross%285%29=cross%28200%2940%2Fcross%285%29
red%28B=40%5Eo%29, substitute in 1st condtn

A=3%2A40%5Eo
red%28A=120%5Eo%29
Also in 2nd contn.
C=40-20
red%28C=20%5Eo%29

Check,
A%2BB%2BC=180%5Eo ---> 120%2B40%2B20=180
180%5Eo=180%5Eo

Thank you,
Jojo

Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
first angle = x
second angle = y
third angle = z
x = 3y
z = y - 20
in a triangle, the sum of its angles are 180 degrees
x + y + z = 180
3y + y + y - 20 = 180
5y - 20 = 180
5y = 180 + 20
5y = 200
y = 200/5
y = 40
x = 3y = 3 * 40 = 120
z = y - 20 = 40 - 20 = 20
so,
the first angle is 120 degrees
the second angle is 40 degrees
the third angle is 20 degrees

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
In a triangle, the first angle measures 3 times the second and the third measures 20 degress less than the second. find each angle's measure.
.
To answer this question, you need to know that the sum of the interior angles of any triangle is 180 degrees.
.
Let x = measure of second angle
then
3x = measure of first angle
3x-20 = measure of third angle
.
x + 3x + 3x-20 = 180
7x-20 = 180
7x = 200
x = 28.57 degrees (second angle)
.
First angle:
3x = 3(28.57) = 85.71 degrees (first angle)
.
Third angle:
3x-20 = 3(28.57)-20 = 65.71 degrees (third angle)