The diagram shows a triangle.
49°
v–8°
31°
What is the value of v?

To solve for \( v \) in the given triangle, we use the fact that the sum of all interior angles in any triangle is always \( 180^\circ \).

Given the three angles in the triangle:
- One angle is \( 49^\circ \),
- Another angle is \( 31^\circ \),
- The third angle is \( v - 8^\circ \).

The sum of these angles must equal \( 180^\circ \), so we can set up the equation:

\[
49^\circ + 31^\circ + (v - 8^\circ) = 180^\circ
\]

Now, let's solve this equation step-by-step:

1. Combine the known angles:
\[
49^\circ + 31^\circ = 80^\circ
\]

2. Substitute this into the equation:
\[
80^\circ + (v - 8^\circ) = 180^\circ
\]

3. Simplify further:
\[
v - 8^\circ + 80^\circ = 180^\circ
\]
\[
v + 72^\circ = 180^\circ
\]

4. Subtract \( 72^\circ \) from both sides:
\[
v = 180^\circ - 72^\circ
\]
\[
v = 108^\circ
\]

Thus, the value of \( v \) is \( 108^\circ \).

Would you like more details or have any further questions?

Here are 5 related questions for you to explore:
1. What is the sum of the interior angles in a quadrilateral?
2. How can we find the exterior angles of a triangle?
3. If one angle in a triangle is \( 90^\circ \), what is the type of triangle?
4. How do we classify triangles based on their angles?
5. Can two angles in a triangle be obtuse?

**Tip:** In any triangle, the sum of the interior angles always adds up to 180°.

The diagram shows a triangle. 49°, v - 8°, 31°. What is the value of v?

Learn how to find the value of v in a triangle with angles 49°, v - 8°, and 31°. This problem uses the angle sum theorem and provides a step-by-step solution. Perfect for students in Grades 6-8 studying geometry.

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