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A pentagon has interior angles of 4m, 5m + 36°, 4m, and 6m. Find the value of m and the measure of each interior angle.

Mathematics

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Step-by-step solution

2 steps
  1. Determine the sum of interior angles of a pentagon.

    The sum of interior angles for an nn-sided polygon is (n−2)×180∘(n-2) \times 180^\circ. For a pentagon, n=5n=5.

    Sum of angles=(5−2)×180∘=3×180∘=540∘\text{Sum of angles} = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
  2. Identify the given angles from the diagram.

    The angles are 4m4m, 5m+36∘5m + 36^\circ, 4m4m, and 6m6m. The fifth angle at the top vertex is marked with an arc but not explicitly labeled with an expression.
    Assumption: Given that two angles are $

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