To find the two unknown angle measures that form the 90° angle, we will set up the following equation based on the sum of angles.
If we have two angles, \((x + 4)°\) and \((3x + 2)°\), and together these angles sum up to 90 degrees, we can form the equation:
\[ (x + 4) + (3x + 2) = 90 \]
Now, simplify the equation:
\[ x + 4 + 3x + 2 = 90 \]
\[ 4x + 6 = 90 \]
Next, subtract 6 from both sides:
\[ 4x = 90 - 6 \] \[ 4x = 84 \]
Now, divide both sides by 4:
\[ x = \frac{84}{4} \] \[ x = 21 \]
Now we can substitute \(x\) back into the expressions for the angles:
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For \((x + 4)°\): \[ (21 + 4)° = 25° \]
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For \((3x + 2)°\): \[ (3 \cdot 21 + 2)° = (63 + 2)° = 65° \]
So, the two unknown angle measures that form the 90° angle are:
\[ (x + 4)° = 25°, \quad (3x + 2)° = 65° \]
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