an illustation shows three rays extending from a common origin. The angle measures between them are labeled (x+4)degrees and (3x+2)degrees. what are the two unknown angle measures that form the 90 degree angle

Answer 1

To find the unknown angle measures that form a 90-degree angle, we need to set up an equation.

The sum of the angle measures in a triangle is 180 degrees. Therefore, we have the equation:

(x+4) + (3x+2) + Unknown Angle = 180

To find the unknown angle measures, we need to solve this equation.

First, combine like terms:

4x + 6 + Unknown Angle = 180

Next, subtract 6 from both sides:

4x + Unknown Angle = 174

Now, for the angle measures to form a 90-degree angle, the sum of the two unknown angles must equal 90 degrees.

Therefore, we can set up a second equation:

Unknown Angle + Unknown Angle = 90

Simplifying this equation, we get:

2 * Unknown Angle = 90

Dividing both sides by 2, we find:

Unknown Angle = 45

Therefore, the two unknown angle measures that form a 90-degree angle are 45 degrees each.