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Angles in Triangles and Polygons (including Tessellation): Worksheets with AnswersWhether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers. Contents
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Worksheet for students to put all the information together for calculating interior and exterior angles of interior and exterior polygons ReviewsSomething went wrong, please try again later. This resource hasn't been reviewed yet To ensure quality for our reviews, only customers who have downloaded this resource can review it Report this resourceto let us know if it violates our terms and conditions. Interior and Exterior Angles Worksheets, Questions and RevisionGCSE 4 - 5KS3AQAEdexcelOCRWJECFoundation Interior and Exterior AnglesThe interior angles of a shape are the angles inside the shape. The exterior angles are the angles formed between a side-length and an extension. Rule: Interior and exterior angles add up to 180\degree. Having the ability to rearrange equations will help with interior and exterior angle questions.
Level 4-5 GCSE  Exterior AnglesRule: The exterior angle = \dfrac{360\degree}{\textcolor{red}{n}} where \textcolor{red}{n} is the number of sides. The sum of all the exterior angles will equal 360\degree. For the triangle shown, we can see it has \textcolor{red}{3} sides, so to calculate an exterior angle we do: \dfrac{360\degree}{\textcolor{red}{3}} = 120\degree Level 4-5 GCSE Interior AnglesRule: Sum of interior angles = (\textcolor{red}{n} - 2) \times 180\degree Where \textcolor{red}{n} is the number of sides. To find the sum of the interior angles for the triangle shown we do the following: (\textcolor{red}{3} - 2) \times 180\degree = 180\degree This means that \textcolor{limegreen}{a} + \textcolor{limegreen}{b} + \textcolor{limegreen}{c} = 180\degree Note: You can find the interior angle of a regular polygon by dividing the sum of the angles by the number of angles. You can also find the exterior angle first then minus from 180\degree to get the interior angle. Level 4-5 GCSE Example: Finding Interior and Exterior AnglesABCD is a quadrilateral. Find the missing angle marked x. [2 marks] This is a 4-sided shape, to work out the interior angles we calculate the following: (\textcolor{red}{n}-2)\times 180 =360\degree. Next we can work out the size of \angle CDB as angles on a straight line add up to 180\degree. 180 - 121 = 59\degree Now we know the other 3 interior angles, we get that x = 360 - 84 - 100 - 59 = 117\degree Level 4-5 GCSE Example QuestionsThis shape has 5 sides, so its interior angles add up to, 180 \times (5 - 2) = 540\degree Hence each interior angle is, x\degree=540\degree \div 5 = 108\degree This shape has 8 sides, so its interior angles add up to, 180 \times (8 - 2) = 1080\degree Hence each interior angle is, x\degree=1080\degree \div 8 = 135\degree
This shape has 5 sides, so its interior angles must add up to 180 \times (5 - 2) = 540\degree. We can’t find this solution with one calculation as we did previously, but we can express the statement “the interior angles add up to 540” as an equation. This looks like 33 + 140 + 2x + x + (x + 75) = 540 Now, this is a linear equation we can solve. Collecting like terms on the left-hand side, we get 4x + 248 = 540. Subtract 248 from both sides to get 4x = 292. Finally, divide by 4 to get the answer: x = 292 \div 4 = 73\degree
This shape has 4 sides, so its interior angles add up to 180 \times (4 - 2) = 360\degree. We don’t have any way of expression two of the interior angles at the moment, but we do have their associated exterior angles, and we know that interior plus exterior equals 180. So, we get \text{interior angle CDB } = 180 - (y + 48) = 132 - y Furthermore, we get \text{interior angle CAB } = 180 - 68 = 112 Now we have figures/expressions for each interior angle, so we write the sum of them equal to 360 in equation form: 112 + 90 + 2y + (132 - y) = 360 Collecting like terms on the left-hand side, we get y + 334 = 360 Then, if we subtract 334 from both sides we get the answer to be y = 360 - 334 = 26\degree. Worksheet and Example QuestionsDrill QuestionsYou May Also Like...GCSE Maths Revision CardsRevise for your GCSE maths exam using the most comprehensive maths revision cards available. These GCSE Maths revision cards are relevant for all major exam boards including AQA, OCR, Edexcel and WJEC. The profit from every pack is reinvested into making free content on MME, which benefits millions of learners across the country. £8.99 View Product GCSE Maths Revision GuideThe MME GCSE maths revision guide covers the entire GCSE maths course with easy to understand examples, explanations and plenty of exam style questions. We also provide a separate answer book to make checking your answers easier! The profit from each revision guide is reinvested into making free content on MME, which benefits millions of learners across the country. From: £14.99 View Product GCSE Maths Predicted Papers 2023GCSE Maths Predicted Papers are perfect for preparing for your GCSE Maths exams. These papers are in the same style and format as real exams. They are only available on MME! The profit from every pack is reinvested into making free content on MME, which benefits millions of learners across the country. From: £5.99 View Product WJEC GCSE Maths Predicted Papers 2023WJEC GCSE Maths Predicted Papers are great preparation for your GCSE Maths exams in 2023. These predicted papers are in the same format and style as the real exams, and come in A4 booklets. Exclusive to MME! The profit from every set is reinvested into making free content on MME, which benefits millions of learners across the country. £5.99 View Product MME Learning PortalOnline exams, practice questions and revision videos for every GCSE level 9-1 topic! No fees, no trial period, just totally free access to the UK’s best GCSE maths revision platform. 100% Free, Forever. View Product Where next?How do you find the interior and exterior angles of a polygon?The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.
What is the sum of interior and exterior angles of a polygon?The sum of an adjacent interior angle and exterior angle for any polygon is equal to 180 degrees since they form a linear pair. Also, the sum of exterior angles of a polygon is always equal to 360 degrees.
How do you find the interior angles of a polygon?Lesson Summary
A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.
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Interior and exterior angles of polygons worksheet
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