angles of a triangle

Question

In a triangle, the measure of the first angle is twice of the 2nd angle. The measure of the third angle is 96 degrees more than the second angle. Use the fact that the sum of the measures of all three angles of a triangle is 180 to find the measure of each angle

Answer 1

Good Afternoon, Maleah,

Allow the second angle to be x 
Allow the first angle to be 2x <-----the measure of second angle is twice the 2'nd angle
Allow the third angle to be x + 96 <----the measure of the third angle is 96 MORE than the second

All angles added together must equal 180, right? Therefore: Solve for x

x + 2x + (x + 96) = 180
3x + x + 96 = 180
4x + 96 = 180 
4x =84 
x = 21   This is the measure of the second angle 

Then plug value of x to determine measure of third angle

x + 96  <---Plug 21 for x
21 + 96 = 117  This is the measure of the third angle.


Then, plug value of x for measure of second angle: 

2(21) =42 This is the measure of the second angle. 

In order to check your work, you need to make sure the three angles added together equal 180. 


Therefore, does 21 plus 42 plus 117 equal 180? 

      21
      42
     117
---------
    180   CHECK! 


Therefore, the measures of each angle are as follows:

∠2 = 21
∠1 = 42
∠3 = 117


I hope this assists. Please feel free to ask any further questions or feedback immediately beneath this question in the comment section, or contact any tutor for further information.