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how to find measures of a triangle whos second angle is 7 more than the first angle,the third angle is 23 more than three times the first angle

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4 Answers

You already know that all the angles of a triangle add up to 180, so you already have one piece of the puzzle completed. Put 180 on one side of the question.


?????? = 180


All you need in order to solve this problem is a little bit of algebra.

 

Let x represent one of the three angles.


Our first angle is simply x

The second angle is 7 more than the first angle (x +7)


The third angle is 23 more than three times the first angle, which is three times X, plus 23 (3x+23)

 

Now all you need to do is put the equation together:

x + (x+7) + (3x+23) = 180


Now solve for x:


5x + 7 + 23 = 180

5x + 30 = 180

5x = 150

x = 30

Now let's see what each angle is when we put in 30 for x, the first angle. If it adds up to 180, that's a good sign we're right.


First angle: 30

Second angle: 30+7 = 37

Third angle: 3(30)+23 = 113

30+37+113 = 180

First, you need to know that the sum of the angles of a triangle equals 180 degrees. Now, translate the words into math:

1st angle = x

2nd angle = x+7

3rd angle = 3x+23

Now, add up the angles in terms of x:

x+x+7+3x+23=180

5x+30=180

5x=150

x=30

So, 1st angle=30, 2nd angle=37, and the 3rd angle=113, which all add up to 180.

 

Joshua, this is an algebra problem hiding as a geometry problem.

If you label the three angles of the triangle a (first angle), b (second angle), and c (third angle).  Then, translate the two sentences into equations, using a, b, and c, instead of 1st, 2nd and third angle.  This will give you two equations and three unknowns.  Additionally, you know that the sum of the angles of a triangle equals how many degrees, (a+b+c=??)?  This will give you three equations and three unknowns, which should have a unique solution.

If you need help translating the sentences, I'll be happy respond to a follow-up question.

Jonasha, how many degrees do the three angles of a triangle equal? The answer is 180°.

Let's call the first angle x.

What do you know about the second angle? You know that it is 7 more that tne first angle. Let's call the second angle x + 7.

What do you know about the third angle? You know that it is 23 more than 3 times the first angle. Let's call the third angle 3x + 23.

All three of these angles must total 180, so we can set up the following equation:

x + x + 7 + 3x + 23 = 180

x + x + 3x = 5x   and   7 + 23 = 30    so we can write the equation as 5x + 30 = 180.

Now you want to subtract 30 from both sides of the equation:  5x + 30  - 30 = 5x and 180 - 30 = 150   so we can now write the equation as 5x = 150.

To solve for x, you now have to divide both sides of the equation by 5: 5x/5 = x  and   150/5 = 30.

x = 30

Now you can determine the degrees of each angle.

The first angle is x, so the first angle measures 30°.  The second angle is x + 7, so the second angle measures 37°.   The third angle is 3x + 23, so the third angle measures 113°.  Now add the three angles to make sure they total 180:  30 + 37 + 113 = 180.

Hope this helps.

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