Use the image to answer the question. 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)°= °

1 answer

To find the unknown angle measures that form a 90° angle, we can set up the equation based on the information given.

We know that the sum of the angles that form a right angle is 90°. Assuming the angles are (x + 4)° and (3x + 2)°, we can set up the equation:

\[ (x + 4) + (3x + 2) = 90 \]

Now, let's combine like terms:

\[ x + 4 + 3x + 2 = 90 \] \[ 4x + 6 = 90 \]

Next, we can subtract 6 from both sides:

\[ 4x = 90 - 6 \] \[ 4x = 84 \]

Then we divide by 4 to solve for \( x \):

\[ x = \frac{84}{4} = 21 \]

Now, we will substitute \( x \) back into the expressions for the angles to find their measures.

  1. For the first angle: \[ (x + 4)° = (21 + 4)° = 25° \]

  2. For the second angle: \[ (3x + 2)° = (3 \times 21 + 2)° = (63 + 2)° = 65° \]

Thus, the two unknown angle measures that form the 90° angle are \( 25° \) and \( 65° \).