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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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 formula

Show source

α=\pi-β-γ

Result

Show source

\frac{\pi}{2}

Numerical result

Show 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).

Tags and links to this website#

Tags:

sum_of_angles_in_triangle · triangle_sum_of_angles

Tags to Polish version:

suma_katow_w_trojkacie · trojkat_suma_katow

What tags this calculator has#

CALCULATOR · MATH · A -> Z (all)

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