The problem presents a triangle where the sum of the angles is 180°. The angles in the triangle are given as 110°, $5x^\circ$, and $2x^\circ$. We can solve for $x$ using the angle sum property of triangles.

Step 1: Set up the equation

The sum of the angles in any triangle is always 180°. Therefore, we can write: $110^\circ + 5x^\circ + 2x^\circ = 180^\circ$

Step 2: Solve for $x$

Combine like terms: $110^\circ + 7x^\circ = 180^\circ$ Now subtract 110° from both sides: $7x^\circ = 70^\circ$ Finally, divide by 7: $x = 10^\circ$

Step 3: Find the values of $5x$ and $2x$

• $5x = 5 \times 10^\circ = 50^\circ$
• $2x = 2 \times 10^\circ = 20^\circ$

Final Answer:

• $x = 10^\circ$
• $5x = 50^\circ$
• $2x = 20^\circ$

Would you like further clarification on any of the steps?

Related Questions:

1. What is the general formula for the sum of angles in any polygon?
2. How do you calculate the angles of a regular polygon?
3. Can you apply the same method to find angles in quadrilaterals?
4. What are alternate methods for finding missing angles in a triangle?
5. How do angle measures change when extending the sides of polygons?

Tip:

Always remember that the sum of the interior angles of a triangle is 180°, which is a useful property for solving many geometric problems.