5. Systems With Three Variables
Sign In
x=36^(∘)
y=72^(∘)
z=108^(∘)
We have been given a regular five-pointed star.
Because the figure is a regular five-pointed star, we have a regular pentagon in the center of the figure.
Using the angles on the figure, we will write three equations on an organized table.
Verbal Expression | Algebraic Expression |
---|---|
Sum of the interior angles of a triangle is 180^(∘). | x+y+y=180 |
Sum of the interior angles of a pentagon is 540^(∘). | z+z+z+z+z=540 |
Sum of two adjacent angles on a straight line is 180^(∘). | y+z=180 |
(I), (II): Add terms
(II): .LHS /5.=.RHS /5.
(III): z= 108
(III): LHS-108=RHS-108
(I): y= 72
(I): Multiply
(I): LHS-144=RHS-144