To find the value of $x$ in the triangle, we can use the angle sum property of a triangle, which states that the sum of the angles in any triangle is always $180^\circ$.

Given:

• One angle is $42^\circ$,
• Another angle is $87^\circ$,
• The third angle is $x^\circ$.

The sum of the angles in the triangle is: $42^\circ + 87^\circ + x^\circ = 180^\circ$

Now solve for $x$: $x = 180^\circ - (42^\circ + 87^\circ)$ $x = 180^\circ - 129^\circ = 51^\circ$

Thus, the value of $x$ is $51^\circ$.

Would you like further clarification on this problem or the reasoning behind the angle sum property?

Here are some additional questions related to this topic:

1. What is the angle sum property for quadrilaterals?
2. Can the sum of angles in any triangle ever be greater than 180°?
3. How can we classify this triangle based on its angles?
4. How can we apply this property in a non-Euclidean geometry?
5. What happens to angle sums in a triangle on a curved surface?

Tip: When solving for unknown angles in any polygon, always remember that the sum of angles in a triangle is always 180°.