What are the sums of angles in common geometric shapes? While we usually use a protractor, a D-shaped instrument in our geometry box to measure the angles, there are other ways of doing that. You will not always have that in your hand to measure them. Moreover, there are chances of human error when you measure them this way. Well, in regular geometric shapes, the angle measurements are fixed, and this helps in reducing the time required to solve an angle-related problem. Talking about triangles, the sum of the interior angles of this shape is equal to 180°. Whether it's an isosceles, scalene, equilateral triangle, also, each angle in the equilateral triangle is equal to 60°. Coming to quadrilaterals, the interior angles of these shapes add up to 360°. The Interior Angles of a Pentagon add up to 540°. The rule here is, with one side added to the shape, another 180° to the total. A triangle has a sum of interior angles equal to 180°, adding one line makes it a quadrilateral, and the sum becomes equal to 360°, add another line ti becomes a pentagon with the sum equal to 540°.

We will look at what angles we can make sense of when two or more lines intersect. We can use what we know about a circle to help us find all the measures of the angles. The sum of all of them in any circle measures 360 degrees. If you look carefully you can see how intersecting lines and circles follow the same type of system. Using this technique and knowing that our sum is 360 degrees, we can easily break off the measure of each angle.
These worksheets explain how to calculate these sums. Your students will use these worksheets to learn how to measure given angles within a circle, and how to check their answers (i.e., all measurements must add up to 360 degrees).