# 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.

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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

2. x+(3y-22)=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

x+y=100

x+3y=202

Now multiply the first equation by -1 on both sides

-x-y=-100

x+3y=202

Now add like terms from eq 1 and eq 2

0+2y=102

Divide new eq by 2 on each side

2y/2 = 102/2

y=51