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

# Beta version#

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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

# What do you want to calculate today?#

 Choose a scenario that best fits your needs I know β and γ and I want to calculate αI know α and γ and I want to calculate βI know α and β and I want to calculate γ

# Calculations data - enter values, that you know here#

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

# Result: First angle (α)#

Summary
Used formulaShow source$α=\pi-β-γ$
ResultShow source$\frac{\pi}{2}$
Numerical resultShow source$1.5707963267948965$
Result step by step
 1 Show source$\pi-\frac{\pi}{4}-\frac{\pi}{4}$ Collect and combine like terms Separability of multiplication with respect to addition allows us to bring-out a common coefficient before the parenthesis: $a \cdot x + b \cdot x = (a + b) \cdot x$ 2 Show source$1~\pi+\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \left(-\pi\right)$ Simplify signs Multiply of two negative numbers gives the possitive one: $-a \cdot (-b) = a \cdot b$ 3 Show source$1~\pi-\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \pi$ Multiply by one Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$ 4 Show source$\pi-\left(\frac{1}{4}+\frac{1}{4}\right) \cdot \pi$ Added fractions To add a fractions with the same denominator we just need add numerators of both fractions: $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ 5 Show source$\pi-\frac{1+1}{4} \cdot \pi$ Simplify arithmetic - 6 Show source$\pi-\frac{2}{4}~\pi$ Multipled fractions To multiply two fractions we need to multiply numberators and denominators from first and second fractions: $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ 7 Show source$\pi+\frac{\cancel{-2}~\pi}{\cancel{4}}$ Cancel terms or fractions Dividing a number by itself gives one, colloquially we say that such numbers "cancel-out": $\frac{\cancel{a}}{\cancel{a}} = 1$to find-out the simplest form of fraction we can divide the numerator and denominator by the greatest common divisor (GCD) of both numbers. 8 Show source$\pi-\frac{1}{2}~\pi$ Collect and combine like terms Separability of multiplication with respect to addition allows us to bring-out a common coefficient before the parenthesis: $a \cdot x + b \cdot x = (a + b) \cdot x$ 9 Show source$\left(1-\frac{1}{2}\right) \cdot \pi$ Added fractions To add a fractions with the same denominator we just need add numerators of both fractions: $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ 10 Show source$\frac{1 \cdot 2-1}{2} \cdot \pi$ Multiply by one Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$ 11 Show source$\frac{2-1}{2} \cdot \pi$ Multipled fractions To multiply two fractions we need to multiply numberators and denominators from first and second fractions: $\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}$ 12 Show source$\frac{\left(2-1\right) \cdot \pi}{2}$ Simplify arithmetic - 13 Show source$\frac{1~\pi}{2}$ Multiply by one Any number multiplied by one (1) gives the same number: $a \cdot 1 = 1 \cdot a = a$ 14 Show source$\frac{\pi}{2}$ Result Your expression reduced to the simplest form known to us.
Numerical result step by step
 1 Show source$1.5707963267948965$ The original expression - 2 Show source$1.5707963267948965$ Result Your 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.
$\alpha + \beta + \gamma = \pi = 180 ^\circ$
• 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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