1. **State the problem:** We need to find the value of $x$ in a triangle where the angles are $60^\circ$, $3x$, and $x + 90^\circ$. Note that the problem mentions an angle labeled $x$ as well, but since a triangle has only three angles, we consider the three given: $60^\circ$, $3x$, and $x + 90^\circ$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is always $180^\circ$. 3. **Set up the equation:** $$ 60 + 3x + (x + 90) = 180 $$ 4. **Simplify the equation:** $$ 60 + 3x + x + 90 = 180 $$ $$ 60 + 90 + 4x = 180 $$ $$ 150 + 4x = 180 $$ 5. **Isolate $x$:** $$ 4x = 180 - 150 $$ $$ 4x = 30 $$ 6. **Divide both sides by 4:** $$ \cancel{4}x = \frac{30}{\cancel{4}} $$ $$ x = \frac{30}{4} = 7.5 $$ 7. **Final answer:** $$ x = 7.5 $$ This means the value of $x$ is 7.5 degrees.