To solve for $x$ in this triangle problem, we can use the fact that the sum of the interior angles of a triangle is always $180^\circ$.

Given angles:

• One angle is $65^\circ$,
• Another angle is $73^\circ$,
• The third angle is $x$.

Solution Steps

1. Set up the equation for the sum of the angles: $65^\circ + 73^\circ + x = 180^\circ$

2. Combine the known angles: $138^\circ + x = 180^\circ$

3. Solve for $x$ by subtracting $138^\circ$ from both sides: $x = 180^\circ - 138^\circ$ $x = 42^\circ$

Answer

The value of $x$ is $42^\circ$.

Would you like a detailed explanation of any of these steps, or do you have further questions?

Here are five related questions for practice:

1. What is the measure of the third angle if two angles in a triangle are $50^\circ$ and $60^\circ$?
2. If a triangle has angles $30^\circ$ and $45^\circ$, what is the measure of the third angle?
3. Can a triangle have two angles of $90^\circ$? Why or why not?
4. If the angles in a triangle are $x$, $x + 20^\circ$, and $2x$, how can you find the value of $x$?
5. What are the properties of an equilateral triangle in terms of angle measures?

Tip: Remember, the sum of the angles in any triangle is always $180^\circ$, which can help you solve similar problems quickly.