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.

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)   (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

It follows ---> , working eqn.

First condition:
The first angle measures 3 times the second:

Second condition:
The third measures 20 degrees less than the second:

Substituting to the working eqn,

--->
, substitute in 1st condtn

Also in 2nd contn.

Check,
--->

Thank you,
Jojo

Answer by alicealc(293)   (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)   (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)
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