Math Problem Statement

What is the value of z in the triangle, given the angles: 2z, 8z - 31°, 25c - 26° and 11z - 47°?

Solution

The problem in the image shows a triangle with three angle expressions involving zz and cc. The interior angles of any triangle sum to 180°. Let's analyze the angles provided in the image.

The angles are:

  1. 2z2z (bottom left angle)
  2. 8z318z - 31^\circ (top angle)
  3. 25c2625c - 26^\circ and 11z4711z - 47^\circ (bottom right angle, exterior)

For the internal angles of a triangle:

  • The sum of the internal angles should equal 180°.
  • Using this, we can solve for zz, since there are two expressions involving zz, but one exterior angle, which also uses zz.

I will now calculate zz, assuming we focus on expressions directly related to zz and the interior angles. Please confirm if the variable cc is needed for calculation or if it's meant to focus just on zz.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Angle Sum Property of Triangles

Formulas

Sum of interior angles of a triangle = 180°
Exterior angle = sum of two opposite interior angles

Theorems

Angle Sum Property
Exterior Angle Theorem

Suitable Grade Level

Grades 9-11