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

March 27, 2026Mathematics

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March 27, 2026

Answer

5$.

Step 1: Determine the sum of interior angles of a pentagon. The sum of interior angles for an $n$ -sided polygon is $(n-2) \times 180^\circ$ . For a pentagon, $n=5$ . $Sum of angles = (5-2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$ Step 2: Identify the given angles from the diagram. The angles are $4m$ , $5m + 36^\circ$ , $4m$ , and $6m$ . 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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Determine the sum of interior angles of a pentagon. The sum of interior angles for an n-sided polygon is (n-2) × 180^.

Asked on March 27, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 27, 2026

Step 1: Determine the sum of interior angles of a pentagon. The sum of interior angles for an n-sided polygon is (n-2) × 180^. For a pentagon, n=5. Sum of angles = (5-2) × 180^ = 3 × 180^ = 540^ Step 2: Identify the given angles from the diagram. The angles are 4m, 5m + 36^, 4m, and 6m. 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 $