Subjects geometry

Angles Polygons A35Fc7

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1. The problem asks to measure one interior angle in each polygon. 2. The sum of interior angles in a polygon with $n$ sides is given by the formula: $$\text{Sum of interior angles} = (n-2) \times 180^\circ$$ This helps us understand the total degrees inside the polygon. 3. For each polygon: - Pentagon ($n=5$): Sum of interior angles = $(5-2) \times 180 = 3 \times 180 = 540^\circ$ - Quadrilateral ($n=4$): Sum of interior angles = $(4-2) \times 180 = 2 \times 180 = 360^\circ$ - Triangle ($n=3$): Sum of interior angles = $(3-2) \times 180 = 1 \times 180 = 180^\circ$ 4. Since the images are not provided, the exact measured angles cannot be given numerically here. However, the method to find each interior angle if regular is: $$\text{Each interior angle} = \frac{\text{Sum of interior angles}}{n}$$ 5. For labeling angles in polygons (Question 2), the rules are: - Right angle: $90^\circ$, marked with a small square. - Acute angle: less than $90^\circ$, marked with A. - Obtuse angle: between $90^\circ$ and $180^\circ$, marked with O. - Reflex angle: greater than $180^\circ$, marked with R. 6. For measuring angles in triangles (Question 3), the sum is always $180^\circ$. If two angles are known, the third can be found by: $$\text{Third angle} = 180^\circ - (\text{angle 1} + \text{angle 2})$$ Since no numerical values or images are provided, the exact answers cannot be computed here. Final note: To solve these problems, measure the angles using a protractor or calculate using the formulas above based on the polygon type and given angles.