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In the triangle \( ABC \), we are given the following angles:

- \( \angle A = 70^\circ \)
- \( \angle C = 64^\circ \)
- \( \angle B = \theta \) (unknown)

To find \( \theta \), we can use the fact that the sum of angles in any triangle is always \( 180^\circ \). Therefore, we can write the equation:

\[
\theta + 70^\circ + 64^\circ = 180^\circ
\]

Simplifying this:

\[
\theta + 134^\circ = 180^\circ
\]

\[
\theta = 180^\circ - 134^\circ
\]

\[
\theta = 46^\circ
\]

Thus, \( \theta = 46^\circ \).

Let me know if you need further details or explanations! Here are some related questions:

1. What is the exterior angle theorem for triangles?
2. Can a triangle have two angles larger than \(90^\circ\)?
3. What is the relationship between the sides and angles in a triangle?
4. How do you classify triangles based on their angles?
5. Can you apply the Law of Sines to find the sides of this triangle?

**Tip:** The sum of interior angles in any polygon can be calculated using the formula \( (n - 2) \times 180^\circ \), where \( n \) is the number of sides. For triangles, this always results in \( 180^\circ \).

Find the value of angle θ in the triangle ABC where angle A = 70°, angle C = 64°, and angle B = θ.

Solve the triangle ABC where angle A is 70°, angle C is 64°, and the unknown angle θ at B is found using the angle sum property of triangles. Learn the step-by-step solution suitable for students in Grades 6-8.

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