Mathematics 7 Polygons and Angles PDF

MATHEMATICS 7 Good day, Paulinians! God bless you and peace be with you.  MATHEMATICS 7 Opening Prayer  MATHEMATICS 7 Polygons and Angles Week 3  LPO of the week MATHEMATICS 7 LPO2: Courageous, Resourceful EXPLORERS & PROBLEM...

MATHEMATICS 7 Good day, Paulinians! God bless you and peace be with you.  MATHEMATICS 7 Opening Prayer  MATHEMATICS 7 Polygons and Angles Week 3  LPO of the week MATHEMATICS 7 LPO2: Courageous, Resourceful EXPLORERS & PROBLEM SOLVERS I am a courageous, resourceful explorer and problem solver, demonstrating my creativity and charism.  EPO of the week MATHEMATICS 7 EPO5: Take the risk of trying out combinations of data, materials, methods, and techniques to derive and test potential solutions to existing problems even at the risk of criticisms.  ILO of the week MATHEMATICS 7 describe and explain the relationships between angle pairs based on their measures. classify polygons whether they are regular or irregular, and whether they are convex or non-convex.  ILO of the week MATHEMATICS 7 deduce the relationship between the exterior angle and adjacent interior angle of a polygon. Assess and strengthen his/her own mathematical skills in determining the measures of angles and the number of sides of polygons.  Polygons and ANGLES MATHEMATICS 7 Show Me Board  Polygons and ANGLES MATHEMATICS 7 Show Me Board Who Am I? Name the Angles Polygons and ANGLES MATHEMATICS 7 𝑨𝒄𝒖𝒕𝒆 𝑨𝒏𝒈𝒍𝒆 Polygons and ANGLES MATHEMATICS 7 𝑹𝒊𝒈𝒉𝒕 𝑨𝒏𝒈𝒍𝒆 Polygons and ANGLES MATHEMATICS 7 𝑶𝒃𝒕𝒖𝒔𝒆 𝑨𝒏𝒈𝒍𝒆 Polygons and ANGLES MATHEMATICS 7 𝑺𝒕𝒓𝒂𝒊𝒈𝒉𝒕 𝑨𝒏𝒈𝒍𝒆  Polygons and ANGLES MATHEMATICS 7 Classify Me! Tell the difference between the polygons. Regular polygons are both equilateral and equiangular while Irregular polygons are neither equiangular nor equilateral.  Polygons and ANGLES MATHEMATICS 7 Convex or Concave?  Polygons and ANGLES MATHEMATICS 7 Convex or Concave? Convex - at least one of the interior angles is less than 180˚.  Polygons and ANGLES MATHEMATICS 7 Convex or Concave?  Polygons and ANGLES MATHEMATICS 7 Convex or Concave? Concave - if at least one interior angle of a polygon is more than 180˚.  Polygons and ANGLES MATHEMATICS 7 What’s our Label? Describe the relationship of the angle pairs. Adjacent Angles If ∠WYZ and ∠XYZ are adjacent, and the sum of both angles is 80° , What is the measure of ∠𝑋𝑌𝑍 if ∠𝑊𝑌𝑍 = 56°? ∠𝑋𝑌𝑍 = 24°  Polygons and ANGLES MATHEMATICS 7 What’s our Label? Describe the relationship of the angle pairs. Complementary Angles -Adjacent angles that add up to 90° If the two angles are complementary, What is the measure of ∠𝑋? ∠𝑋 = 53°  Polygons and ANGLES MATHEMATICS 7 What’s our Label? Describe the relationship of the angle pairs. Supplementary Angles - Adjacent angles that add up to 180° If the two angles are supplementary, What is the measure of ∠𝑋? ∠𝑋 = 50°  Polygons and ANGLES MATHEMATICS 7 Let’s Analyze!  Polygons and ANGLES MATHEMATICS 7 The exterior angle and the adjacent interior angle of a polygon are supplementary.  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE INTERIOR ANGLES OF AN IRREGULAR POLYGON  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE INTERIOR ANGLES OF AN IRREGULAR POLYGON Steps in Solving: 1. Solve for the sum of interior angles. 2. Add the given interior angles. 3. Subtract the interior angles from the sum.  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE INTERIOR ANGLES OF AN IRREGULAR POLYGON Example 1: 𝟗 − 𝟐 𝟏𝟖𝟎° = 𝟏𝟐𝟔𝟎° 𝟏𝟑𝟓° + 𝟗𝟖° + 𝟏𝟎𝟐° + 𝟏𝟒𝟎° + 𝟐𝟎𝟎° + 𝟏𝟕𝟐° + 𝟏𝟑𝟎° + 𝟏𝟐𝟓° = 𝟏𝟏𝟎𝟐° 𝒙° = 𝟏𝟐𝟔𝟎 − 𝟏𝟏𝟎𝟐° 𝒙° = 𝟏𝟓𝟖°  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE INTERIOR ANGLES OF AN IRREGULAR POLYGON Example 2: If the three interior angles of a quadrilateral are 86°,120°, and 40°, what is the measure of the fourth interior angle? 𝟒 − 𝟐 𝟏𝟖𝟎° = 𝟑𝟔𝟎° 𝟖𝟔° + 𝟏𝟐𝟎° + 𝟒𝟎° = 𝟐𝟒𝟔° 𝒙° = 𝟑𝟔𝟎 − 𝟐𝟒𝟔° 𝒙° = 𝟏𝟏𝟒°  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE INTERIOR ANGLES OF AN IRREGULAR POLYGON Try This!  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE EXTERIOR ANGLES OF AN IRREGULAR POLYGON  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE EXTERIOR ANGLES OF AN IRREGULAR POLYGON Steps in Solving: 1. Add all the given exterior angles. 2. Subtract the sum of the given exterior angles from 360°  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE EXTERIOR ANGLES OF AN IRREGULAR POLYGON Example 1: A scalene triangle has exterior angles measuring 145° and 96°. What is the measure of the third exterior angle? Solution: 360° − 145° + 95° 360° − 240° 𝑀𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑖𝑟𝑑 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = 120°  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE EXTERIOR ANGLES OF AN IRREGULAR POLYGON Example 2: Solution: 360° − 70° + 60° + 65° + 40° 360° − 235° 𝑀𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑖𝑓𝑡ℎ 𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑎𝑛𝑔𝑙𝑒 = 125°  Polygons and ANGLES MATHEMATICS 7 SOLVING FOR THE EXTERIOR ANGLES OF AN IRREGULAR POLYGON Try This!  Polygons and ANGLES MATHEMATICS 7 SOCIO-CULTURAL LINK Angles in Architecture and Design As a courageous, resourceful explorer and problem solver Paulinian, how important is precise angle calculation in building houses or creating designs?  Polygons and ANGLES MATHEMATICS 7 REFLECT AND SHARE As a courageous, resourceful explorer and problem solver Paulinian, how important is knowing different angles of a situation in solving for issues or problems?  Polygons and ANGLES MATHEMATICS 7 LESSON SYNTHESIS It is important to learn how to accurately solve for angles of polygons because it trains us to be precise in calculations whenever we are doing projects. It is also important to recognize different angles and sides of situations to better judge and think of workable solutions to existing problems.  Polygons and ANGLES MATHEMATICS 7 PAULINIAN AFFIRMATION IN CONTEXT I am a courageous, resourceful explorer IN UNDERSTANDING ANGLES AND SIDES OF SITUATIONS, and problem solver, demonstrating my creativity and charism.  MATHEMATICS 7 Closing Prayer