SOLUTION: In the following triangle, the degree measures of the three interior angles and two of the exterior angles are represented with variables. Find the measure of each interior an angl

Algebra ->  Trigonometry-basics -> SOLUTION: In the following triangle, the degree measures of the three interior angles and two of the exterior angles are represented with variables. Find the measure of each interior an angl      Log On


   

Question 923729: In the following triangle, the degree measures of the three interior angles and two of the exterior angles are represented with variables. Find the measure of each interior an angle.

(let me describe the triangle: It is a regular triangle, the bottom right hand corner, the angle is labeled as z and has 2x-5. On the bottom left hand corner, the variable is x but no value. The top of the triangle is y with 2x+5)
any help would be really appreciated
thank you so much in advance
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
we have the following equations
y + 2x+5 = 180
z + 2x-5 = 180
therefore
y = 175 -2x
z = 185 -2x
we know the sum of the interior angles of the regular triangle = 180
now we have
175-2x + 185-2x +x = 180
-3x + 360 = 180
-3x = -180
x = 60
y = 55
z = 65