Example Question - sum of interior angles
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Calculating the Sum of Interior Angles in a Polygon
<p>Let n be the number of sides (or angles) in the polygon.</p> <p>The formula for the sum of the interior angles in an n-sided polygon is:</p> <p>\[ (n - 2) \times 180^\circ \]</p> <p>We are given that one angle measures \( 50^\circ \). As the polygon appears to be a rhombus, all angles are equal.</p> <p>Since there are four angles in total, we can write:</p> <p>\[ 4 \times 50^\circ = (n - 2) \times 180^\circ \]</p> <p>\[ 200^\circ = (n - 2) \times 180^\circ \]</p> <p>The exact question being asked is not clear from the image, but assuming we need to confirm if the angles provided can form a polygon, we can solve for n:</p> <p>\[ n - 2 = \frac{200^\circ}{180^\circ} \]</p> <p>\[ n - 2 = \frac{20}{18} \]</p> <p>\[ n - 2 = 1\frac{1}{9} \]</p> <p>Given that n must be a whole number, the answer 1\(\frac{1}{9}\) indicates that the values presented do not form a consistent set for a polygon with all equal angle measures. Hence, there seems to be a discrepancy unless the intention was to showcase an irregular polygon, in which case additional information would be needed.</p>
Solving Quadrilateral Angles Equation
The image you provided shows a quadrilateral ABCD with its interior angles labeled as follows: - Angle A = x degrees - Angle B = y degrees - Angle C = (2z) degrees - Angle D = (z - 15) degrees The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, to solve for x, y, and z, we can set up the following equation: x + y + (2z) + (z - 15) = 360 Combine like terms: x + y + 3z - 15 = 360 This gives us one equation with three unknowns, which means we cannot uniquely determine the values of x, y, and z without additional information. To solve for these variables, we would need two more independent equations relating them. However, if the question is to express x, y, and z in terms of each other, you could solve one variable in terms of the other two. If that's the case or if there are additional constraints or information, please provide them so that we can assist you further.
Calculating Sum of Interior Angles of Convex Polygon
To find the sum of the interior angles of a convex polygon, you can use the following formula: Sum of interior angles = (n - 2) × 180° where n is the number of sides of the polygon. The polygon in the image appears to be a triangle, which has 3 sides. So we substitute n = 3 into the formula: Sum of interior angles = (3 - 2) × 180° Sum of interior angles = 1 × 180° Sum of interior angles = 180° Therefore, the sum of the interior angle measures of this polygon is 180 degrees.
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