Question 1187447: The angles of a triangle are (2x+20)⁰,(x+25)⁰ and(2x−25)⁰ Given that the sum of the angles of a triangle is 180⁰, calculate the size of each angle
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
As your teacher mentions, the three angles of any triangle add to 180.
angle1+angle2+angle3 = 180
(2x+20)+(x+25)+(2x-25) = 180
2x+20+x+25+2x-25 = 180
(2x+x+2x)+(20+25-25) = 180
5x+20 = 180
5x = 180-20
5x = 160
x = 160/5
x = 32
That x value then leads to...
angle1 = 2x+20 = 2*32+20 = 64+20 = 84 degrees
angle2 = x+25 = 32+25 = 57 degrees
angle3 = 2x-25 = 2*32-25 = 64-25 = 39 degrees
Note how: 84+57+39 = 180 to help confirm the correct answers
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Answers:
angle1 = 2x+20 = 84 degrees
angle2 = x+25 = 57 degrees
angle3 = 2x-25 = 39 degrees
x = 32
Side note: This triangle is acute because all three angles are less than 90. The triangle is also scalene because the three angles are all different from each other.
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