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Find the unknown angle in the following triangles write the missing angle and the type of triangle on the lines below each triangle

We are given a triangle with two angles marked as \( 31^\circ \) and \( 75^\circ \), and we are asked to find the missing angle, denoted by \( x \), and determine the type of triangle.

### Step 1: Calculate the missing angle
In a triangle, the sum of all interior angles is always \( 180^\circ \). Therefore, we can find the unknown angle \( x \) by using the equation:

\[
x + 31^\circ + 75^\circ = 180^\circ
\]

Simplifying this:

\[
x = 180^\circ - (31^\circ + 75^\circ) = 180^\circ - 106^\circ = 74^\circ
\]

So, \( x = 74^\circ \).

### Step 2: Determine the type of triangle
Since all the angles in the triangle are less than \( 90^\circ \), the triangle is **acute** (i.e., all angles are acute angles).

### Final Answer:
- \( x = 74^\circ \)
- Type of triangle: Acute triangle

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:
1. What is the sum of angles in a quadrilateral?
2. Can a triangle have more than one obtuse angle? Why or why not?
3. What defines a right triangle in terms of its angles?
4. How do we classify triangles based on their sides and angles?
5. What is the exterior angle theorem for triangles?

**Tip:** Always double-check the sum of angles in polygons when solving for missing angles to avoid calculation errors.

Find the unknown angle in the following triangle and write the missing angle and type of triangle: Given angles are 31° and 75°.

Learn how to find the missing angle in a triangle where two angles are 31° and 75°. Understand how the Triangle Angle Sum Theorem is applied and determine that the triangle is acute. Suitable for students in Grades 6-8.

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