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 its a triangle

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