To solve this problem, let's follow the steps:

Step 1: Understand the triangle's angle sum property

In any triangle, the sum of the angles is always 180°. This gives us the equation: $96^\circ + 2x + (x + 12) = 180^\circ$

Step 2: Simplify the equation

Combine like terms: $96 + 2x + x + 12 = 180$ $3x + 108 = 180$

Step 3: Solve for $x$

Isolate $x$: $3x = 180 - 108$ $3x = 72$ $x = 24$

Step 4: Find the measures of the requested angles

1. $m\angle x + 12$: $x + 12 = 24 + 12 = 36^\circ$

2. $m\angle 2x$: $2x = 2(24) = 48^\circ$

Final Answers:

• $x = 24^\circ$
• $m\angle x + 12 = 36^\circ$
• $m\angle 2x = 48^\circ$

Would you like further clarification or a detailed explanation of these calculations?

Related Questions:

1. How do you confirm the angle sum property works with the calculated values?
2. What happens if the triangle has obtuse or right angles?
3. Can this method work for solving triangles with missing sides instead of angles?
4. How does this process change if the triangle is isosceles or equilateral?
5. What does solving angles in a non-Euclidean triangle involve?

Tip:

When solving for angles in any triangle, always confirm that the sum equals 180° to verify your calculations.