A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many DUCKS are there?
2 answers:
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Answer:
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Polygons can be regular or irregular. If the angles are all equal and all the sides are equal length it is a regular polygon.
Regular and irregular polygons
Interior angles of polygons
To find the sum of interior angles in a polygon divide the polygon into triangles.
Irregular pentagons
The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
Example
Calculate the sum of interior angles in a pentagon.
A pentagon contains 3 triangles. The sum of the interior angles is:
180 * 3 = 540
The number of triangles in each polygon is two less than the number of sides.
The formula for calculating the sum of interior angles is:
(n - 2) * 180 (where n is the number of sides)
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Answer:
AB = 13.89
Measure of angle A = 59.74°
Measure of angle B = 30.26°
Step-by-step explanation:
The given parameters are;
∠C = 90°
AC = 7
BC = 12
Part 1
Hence, the question has the dimensions of the two adjacent sides of the right angle (angle 90°)
From Pythagoras theorem, we have;
A² = B² + C²
Where, A is the opposite side to the right angle, hence;
In the ΔABC,
AB ≡ A
Therefore;
AB² = AC² + BC² = 7² + 12² = 193
∴ AB = √193 = 13.89
Part 2
∠A is the side opposite side BC such that by trigonometric ratios
∴ ∠A = Arctan(1.714) or tan⁻¹(1.714) = 59.74°
Part 3
∠B is found from knowing that the sum of the angles in a triangle = 180°
∴ ∠A + ∠B + ∠C = 180° which gives
59.74° + 90° + ∠B = 180°
Hence, ∠B = 180° - (59.74° + 90°) = 180° - 149.74° = 30.26°.