An illustration shows three rays extending from a common origin. The angle measures between them are labeled. What are the two unknown angle measures that form the 90° angle? (1 point) (x+4)°= °, (3x+2)°=
Let's call the angles x°, (x+4)°, and (3x+2)°.
Since the three rays extend from a common origin, the sum of the angles formed must be 360°.
So, x° + (x+4)° + (3x+2)° = 360°.
Combining like terms, we get 5x + 6 = 360.
Subtracting 6 from both sides, we get 5x = 354.
Dividing both sides by 5, we get x = 354/5.
Therefore, x = 70.8°.
Now, we can substitute this value back into the equations to find the unknown angle measures.
(x+4)° = 70.8° + 4° = 74.8°.
(3x+2)° = 3(70.8°) + 2° = 212.4° + 2° = 214.4°.
Therefore, the two unknown angle measures that form the 90° angle are:
(x+4)° = 74.8°
(3x+2)° = 214.4°