This problem involves a triangle where the angle measures are expressed in terms of $x$. Let’s solve it step by step.

Step 1: Key Triangle Property

The sum of all angles in a triangle is always $180^\circ$. Therefore: $(4x - 7)^\circ + (3x + 2)^\circ + 142^\circ = 180^\circ$

Step 2: Combine Like Terms

Combine all terms involving $x$ and constants: $4x - 7 + 3x + 2 + 142 = 180$ $7x + 137 = 180$

Step 3: Solve for $x$

Subtract $137$ from both sides: $7x = 43$ Divide by $7$: $x = \frac{43}{7} \approx 6.14$

It seems that this problem's options may not match the solution as presented. Would you like me to confirm your work or clarify next steps? ### Step 1. Triangles angle propertyThis problem involves solving for the value of $x$ in a triangle where the angles are expressed algebraically. The key property to use is that the sum of the interior angles of a triangle is always $180^\circ$.

Step-by-Step Solution:

Step 1: Write the equation

From the diagram: $(4x - 7)^\circ + (3x + 2)^\circ + 142^\circ = 180^\circ$

Step 2: Combine like terms

Combine the $x$-terms and constants: $4x + 3x - 7 + 2 + 142 = 180$ $7x + 137 = 180$

Step 3: Solve for $x$

1. Subtract $137$ from both sides: $7x = 43$
2. Divide by $7$: $x = \frac{43}{7} \approx 6.14$

Conclusion:

The value of $x$ calculated does not directly match the multiple-choice options provided. Could you clarify if there are additional conditions or constraints we might have missed, or if this was a typo in the options? Let me know how you'd like to proceed!