A quadrilateral has the following interior angles: 78°, 130°, 72° 80°. Find the exterior angle
Answers
Answer:
Quick Definitions
Let's go over a few key words so we're all on the same page. Remember that a polygon is a two-dimensional shape with sides drawn by straight lines (no curves) which together form a closed area. Each point on a polygon where two sides meet is called a vertex. At each vertex, there is an interior angle of the polygon. A square, for example, has four interior angles, each of 90 degrees. If the square represented your classroom, the interior angles are the four corners of the room.
Sum of the interior angles
To extend that further, if the polygon has x sides, the sum, S, of the degree measures of these x interior sides is given by the formula S = (x - 2)(180).
For example, a triangle has 3 angles which add up to 180 degrees. A square has 4 angles which add up to 360 degrees. For every additional side you add, you have to add another 180 degrees to the total sum.
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Let's talk about a diagonal for a minute. What is a diagonal anyway? A diagonal is a line segment connecting two nonconsecutive vertices of the polygon. It's all the lines between points in a polygon if you don't count those that are also sides of the polygon. In the picture below, BD is a diagonal. As you can see, line segment BD divides quadrilateral ABCD into two triangles. The sum of the angles in those triangles (180+180=360) is the same as the sum of all the angle measures of the rectangle (360).
Answer:
.. interior angle equal to 360° and also exterior angle equal to 360°