Math Problem Statement

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

Solution

In the triangle ABCABC, we are given the following angles:

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

To find θ\theta, we can use the fact that the sum of angles in any triangle is always 180180^\circ. Therefore, we can write the equation:

θ+70+64=180\theta + 70^\circ + 64^\circ = 180^\circ

Simplifying this:

θ+134=180\theta + 134^\circ = 180^\circ

θ=180134\theta = 180^\circ - 134^\circ

θ=46\theta = 46^\circ

Thus, θ=46\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 9090^\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 (n2)×180(n - 2) \times 180^\circ, where nn is the number of sides. For triangles, this always results in 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Sum Property

Formulas

Sum of angles in a triangle: θ + 70° + 64° = 180°

Theorems

Angle Sum Property of Triangles

Suitable Grade Level

Grades 6-8