To find the measures of the two unknown angles that form a 90° angle, we can set up the equation:
\[ (x + 4) + (3x + 2) = 90 \]
Now, simplify the left side of the equation:
\[ x + 4 + 3x + 2 = 90 \]
Combine like terms:
\[ 4x + 6 = 90 \]
Next, subtract 6 from both sides:
\[ 4x = 90 - 6 \] \[ 4x = 84 \]
Now, divide both sides by 4:
\[ x = \frac{84}{4} = 21 \]
Now that we have the value of \(x\), we can find the measures of the two angles.
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The first angle is: \[ x + 4 = 21 + 4 = 25° \]
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The second angle is: \[ 3x + 2 = 3(21) + 2 = 63 + 2 = 65° \]
Thus, the two unknown angle measures are 25° and 65°.