Triangle: sum of angles
Enter two angles and this caltulator will compute third one for you.

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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

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First angle (α)
=>
Second angle (β)
<=
Third angle (γ)
<=

Result: First angle (α)#

Summary
Used formulaShow sourceα=πβγα=\pi-β-γ
ResultShow sourceπ2\frac{\pi}{2}
Numerical resultShow source1.57079632679489651.5707963267948965
Result step by step
1Show sourceππ4π4\pi-\frac{\pi}{4}-\frac{\pi}{4}Collect and combine like termsSeparability of multiplication with respect to addition allows us to bring-out a common coefficient before the parenthesis: ax+bx=(a+b)xa \cdot x + b \cdot x = (a + b) \cdot x
2Show source1 π+(14+14)(π)1~\pi+\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \left(-\pi\right)Simplify signsMultiply of two negative numbers gives the possitive one: a(b)=ab-a \cdot (-b) = a \cdot b
3Show source1 π(14+14)π1~\pi-\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \piMultiply by oneAny number multiplied by one (1) gives the same number: a1=1a=aa \cdot 1 = 1 \cdot a = a
4Show sourceπ(14+14)π\pi-\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \piAdded fractionsTo add a fractions with the same denominator we just need add numerators of both fractions: ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}
5Show sourceπ1+14π\pi-\frac{1+1}{4} \cdot \piSimplify arithmetic-
6Show sourceπ24 π\pi-\frac{2}{4}~\piMultipled fractionsTo multiply two fractions we need to multiply numberators and denominators from first and second fractions: abcd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
7Show sourceπ+2 π4\pi+\frac{\cancel{-2}~\pi}{\cancel{4}}Cancel terms or fractions
  • Dividing a number by itself gives one, colloquially we say that such numbers "cancel-out": aa=1 \frac{\cancel{a}}{\cancel{a}} = 1
  • to find-out the simplest form of fraction we can divide the numerator and denominator by the greatest common divisor (GCD) of both numbers.
8Show sourceπ12 π\pi-\frac{1}{2}~\piCollect and combine like termsSeparability of multiplication with respect to addition allows us to bring-out a common coefficient before the parenthesis: ax+bx=(a+b)xa \cdot x + b \cdot x = (a + b) \cdot x
9Show source(112)π\left(1-\frac{1}{2}\right) \cdot \piAdded fractionsTo add a fractions with the same denominator we just need add numerators of both fractions: ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}
10Show source1212π\frac{1 \cdot 2-1}{2} \cdot \piMultiply by oneAny number multiplied by one (1) gives the same number: a1=1a=aa \cdot 1 = 1 \cdot a = a
11Show source212π\frac{2-1}{2} \cdot \piMultipled fractionsTo multiply two fractions we need to multiply numberators and denominators from first and second fractions: abcd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}
12Show source(21)π2\frac{\left(2-1\right) \cdot \pi}{2}Simplify arithmetic-
13Show source1 π2\frac{1~\pi}{2}Multiply by oneAny number multiplied by one (1) gives the same number: a1=1a=aa \cdot 1 = 1 \cdot a = a
14Show sourceπ2\frac{\pi}{2}ResultYour expression reduced to the simplest form known to us.
Numerical result step by step
1Show source3.1415926535897932\frac{3.141592653589793}{2}Divided fraction-
2Show source1.57079632679489651.5707963267948965ResultYour expression reduced to the simplest form known to us.

Some facts#

  • A triangle is a polygon with three edges and three vertices.
  • The sum of angles in triangle is 180 degrees or π radians.
α+β+γ=π=180\alpha + \beta + \gamma = \pi = 180 ^\circ
  • Due to length of the sides we distinguish below types of triangles:
    • scalene triangle - all sides have different length,
    • isosceles triangle - at least two sides have the same length,
    • equilateral triangle - all sides have the same length.
  • Due to angles measure we distinguish below types of triangles:
    • acute triangle - all angles measure less than 90 degrees (π/2 radians),
    • right triangle - one of angle measures exacly 90 degrees (π/2 radians),
    • obtuse triangle - one of angle measures greater than 90 degrees (π/2 radians).

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