Solve for y. A triangle's three angle measures are: 80 degrees, y degrees, and unknown. The exterior angle next to unknown, measures (3y-22) degrees.
Let the unknown angle be x. Since the exterior angle is the adjacent angle, the sum of x and the adjacen angle is 180.
x + 3y - 22 = 180
x+3y = 202 (1)
We also know that the sum of the angles of a triangle is also 180 degrees.
80 + y + x = 180 (2)
y+x = 100
x+y = 100
To calculate x and y, we'll have to solve the system formed by the equations (1) and (2). We'll use elimination method:
We'll subtract (2) from (1) and we'll get:
x + 3y - y - x = 202-100
We'll combine and eliminate like terms:
2y = 102
y = 51
y = 51 degrees
Assumptions: x = unknown angle, sum of angles in a triangle is 180, sum of adjacent angles is 180.
The first step is to set up 2 equations
1. 80 + y +x = 180
Now simplify each equation independantly
For equation 1, subtract 80 from both sides.
1. x + y = 100
For equation 2, remove parenthesis and add 22 to both sides.
2. x + 3y = 202
Now place bothe equations one above the other
Now multiply the first equation by -1 on both sides
Now add like terms from eq 1 and eq 2
Divide new eq by 2 on each side
2y/2 = 102/2