Since both of them form a linear pair, their sum is always equal to 180°. This formula is used when an interior angle of a quadrilateral is known and the value of the corresponding exterior angle is required. Exterior angle = 180° - Interior angle.There are some basic formulas related to the interior and exterior angles of a quadrilateral. In case, if the quadrilateral is a square or a rectangle, then all its exterior angles will be 90° each.įAQS on Angles of Quadrilateral What is the Formula for Angles of Quadrilateral? For example, if an interior angle of a quadrilateral is 60°, then its corresponding exterior angle will be, 180 - 60 = 120°. Therefore, if one interior angle of a quadrilateral is known, we can find the value of its corresponding exterior angle. If we observe the figure given above, we can see that the exterior angle and interior angle form a straight line, and hence, they make a linear pair. The angles that are formed between one side of a quadrilateral and another line extended from an adjacent side are called its exterior angles. Therefore, the 4th angle = 360 - 240 = 120° Exterior Angles of a Quadrilateral We know that the sum of the interior angles of a quadrilateral is 360°. Using the angle sum property of quadrilaterals, we can find the unknown angles of quadrilateral. In case if the quadrilateral is a square or a rectangle, then we know that all its interior angles are 90° each.Įxample: Find the 4th interior angle of a quadrilateral if the other 3 angles are 85°, 90°, and 65° respectively. This helps in calculating the unknown angles of a quadrilateral. The sum of the interior angles of a quadrilateral is 360°. The angles that lie inside a quadrilateral are called its interior angles. Observe the following figure to understand the difference between the interior and exterior angles of a quadrilateral. There are 4 interior angles and 4 exterior angles in a quadrilateral. Interior and Exterior Angles of Quadrilateral If the other angles are known, then their sum can be subtracted from 360° to get the value of the unknown angle. This property helps in finding the unknown angles of quadrilateral. Therefore, according to the angle sum property of a quadrilateral, the sum of its interior angles is always 360°. For example, let us take a quadrilateral and apply the formula using n = 4, we get: S = (n − 2) × 180°, S = (4 − 2) × 180° = 2 × 180° = 360°. The sum of the interior angles of a polygon can be calculated with the formula: S = (n − 2) × 180°, where 'n' represents the number of sides of the given polygon. To make things easier, this can be calculated by a formula, which says that if a polygon has 'n' sides, there will be (n - 2) triangles inside it. These triangles are formed by drawing diagonals from a single vertex. According to the angle sum property of a polygon, the sum of the interior angles of a polygon can be calculated with the help of the number of triangles that can be formed in it.
This value is obtained using the angle sum property of a quadrilateral. We define $\angle A$ as the quadrilateral angle at $A$ and similarly for the other vertices.ĭraw the diagonal $\overline)\approx-1☃0'19''$ We will, however, allow for concave solutions. We can therefore solve for this angle by rendering its cosine. Wlog we can cyclically permute the sides so that $a+b\ge c+d$, which assures that the angle at $B$ will be between $0°$ and $180°$ (that angle is convex). The sides of quadrilateral $ABCD$ are rendered as $AB=a,BC=b,CD=c,DA=d$ in rotational order, with area $K$. It is assumed here that solutions exist where the quadrilateral does not cross itself, which avoids complications with having to use negative signs for opposite orientations of areas and angles. $a=3, b=4, \theta = 30°$ or $150°$) you can even have the quadrilateral concave for the acute $\theta$ and convex for the obtuse $\theta$. But that means the area is the same for two supplementary values of $\theta$, and except for the obvious degeneracies given by $\theta=90°$ and $a=b$, the kites will have two different shapes. The area is not hard to render as $ab\sin\theta$ where $\theta$ measures either of the congruent angles where an $a$ side meets a $b$ side (divide the quadrilateral in half along its mirror libe and consider each triangle). Imagine a kite with sides $a,b,b,a$ in rotational order.
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