{"id":1287,"date":"2023-09-27T14:16:06","date_gmt":"2023-09-27T14:16:06","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=1287"},"modified":"2023-09-27T14:18:35","modified_gmt":"2023-09-27T14:18:35","slug":"week-3-jss-2-third-term-mathematics-lesson-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-3-jss-2-third-term-mathematics-lesson-notes\/","title":{"rendered":"Week 3 – Jss 2 Third Term Mathematics Lesson Notes"},"content":{"rendered":"

WEEK 3\u00a0\u00a0\u00a0\u00a0ANGLES AND POLYGON
\n<\/strong><\/p>\n

TYPES AND PROPERTIES OF ANGLES
\n<\/h3>\n

Straight Angles
\n\t\tAngles which measure exactly 180\u00b0 (degrees) are straight angles. Therefore, straight angles are straight lines. Angles are represented by the sign \u03f4, called theta. That is, for straight angles, \u03f4= 180\u00b0.
\n\"\"
\n\t\tRight Angles
\n\t\tAngles which measure exactly 90\u00b0 are right angles, that is, \u03f4 = 90\u00b0.
\n\"\"
\n\t\tObtuse Angles
\n\t\tObtuse angles are those which are greater than 90\u00b0 but less than 180\u00b0, that is, 90\u00b0 < \u03f4 < 180\u00b0.
\n\"\"<\/p>\n

\u00a0
\n\u00a0Acute Angles
\n\t\tAcute angles are angles which are greater than 0\u00b0 but less than 90\u00b0, that is, 0\u00b0 < \u03f4 < 90\u00b0.
\n\"\"
\n\t\tReflex Angles
\n\t\tReflex angles are angles which are greater than 180\u00b0 but less than 360\u00b0, that is, 180\u00b0 < \u03f4 < 360\u00b0.
\n\"\"
\n\t\tAdjacent Angles
\n\t\tTwo angles which share the same vertex (centre, usually represented by 0) and have a common side (line) are called adjacent angles.
\n\"\"<\/p>\n

\u00a0
\n\u00a0Complementary Angles
\n\t\tComplementary angles are two angles which when summed equals 90\u00b0.
\n\"\"
\n\t\tNote: <A and <B, are ‘angle A’ and ‘angle B’ respectively.
\nSupplementary Angles
\n\t\tSupplementary angles are two angles which when summed equals 180\u00b0.
\n\"\"
\n\t\tVertically Opposite Angles
\n\t\tVertically opposite angles are the angles opposite to each other when two straight lines intersect. Their defining property is that, vertically opposite angles are equal in magnitude.
\n\"\"
\n\t\tCorresponding Angles
\n\t\tWhen two parallel lines are crossed by a line called the transversal, the angles formed which are in corresponding positions, are called corresponding angles. Corresponding angles are equal in magnitude.
\n\"\"<\/p>\n

\u00a0EXAMPLES: Calculate the size of the marked angle in the diagram below
\n<\/strong>
\n\u00a0\"\"\/\"\"\/\"\"\/\"\"\/
\n\t\t\t<\/strong>\"\"\/\"\"\/ 560 <\/sup> 950<\/sup>
\n\t\t\t<\/strong>\"\"\/ 470<\/sup> x 950 <\/sup> 780<\/sup> x
\n<\/strong>
\n\u00a0
\n\u00a0POLYGON: <\/strong>A part from triangle and quadrilateral, we have other polygons which are also named according to the number of sides they have.
\n Examples are pentagon = 5, Hexagon = 6. It can be regular or irregular. A polygon is said to be regular when all the sides and angles are equal. An irregular polygon has neither of the sides or angles equal. <\/strong><\/p>\n

\u00a0
\n\u00a0TYPES OF POLYGON (Regular Polygons)
\n<\/strong>Regular polygons have all sides, and all angles equal.
\n\"\"\/<\/p>\n

\u00a0
\n\u00a0\"\"\/
\n\t\tSize of Internal Angles
\n\t\tTo find the size of the internal angles of a regular polygon with ‘n’ sides, use the formula:
\n\"\"
\n\t\tFor example, the size of the interior angles of the pentagon (five sides) above is:
\n\"\"
\n\t\tThe sum of all the interior angles of a polygon with ‘n’ sides is found using the formula:
\n(n \u2013 2)\u00a0 x \u00a0180\u00b0
\nTherefore, the sum of all the interior angles of the pentagon above is:
\n(5 \u2013 2)\u00a0 x 180\u00b0\u00a0 =\u00a0 3\u00a0 x 180\u00b0\u00a0 =\u00a0 540\u00b0
\nSize of Exterior Angles
\n\t\tInterior and Exterior angles are measured on the same line, that is, they add up to 180\u00b0.
\nTherefore, the size of an exterior angle =\u00a0 180\u00b0 \u2013 Interior angle.
\nFor example, the size of the external angle of the pentagon above is:
\nSince, interior angle = 108\u00b0
\nThen, exterior angle =\u00a0 180\u00b0 \u2013 Interior angle
\n180\u00b0 \u2013 108\u00b0 =\u00a0 72\u00b0
\nBelow is a list of the names and the number of sides, of some of the most popular polygons.<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n
Name of Polygon<\/strong><\/td>\nNumber of Sides<\/strong><\/td>\n<\/tr>\n
Equilateral Triangle<\/td>\n3<\/td>\n<\/tr>\n
Quadrilateral<\/td>\n4<\/td>\n<\/tr>\n
Pentagon<\/td>\n5<\/td>\n<\/tr>\n
Hexagon<\/td>\n6<\/td>\n<\/tr>\n
Heptagon<\/td>\n7<\/td>\n<\/tr>\n
Octagon<\/td>\n8<\/td>\n<\/tr>\n
Nonagon<\/td>\n9<\/td>\n<\/tr>\n
Decagon<\/td>\n10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

\u00a0DO THESE:<\/p>\n

    \n
  • \n
    Calculate the total internal angle of an octagon\n<\/div>\n<\/li>\n
  • \n
    The size of each angle of a regular octagon\n<\/div>\n<\/li>\n
  • \n
    The total internal of decagon\n<\/div>\n<\/li>\n
  • \n
    The size of each angle of a regular decagon.\n<\/div>\n<\/li>\n<\/ul>\n

    ASSIGNMENT:
    \nPAGE 233 EXERCISE 18.3 QUESTION 1 TO 10 OF ESSENTIAL MATHEMATICS FOR JUNIOR SECONDARY SCHOOLS BOOK 2<\/p>\n","protected":false},"excerpt":{"rendered":"

    WEEK 3\u00a0\u00a0\u00a0\u00a0ANGLES AND POLYGON TYPES AND PROPERTIES OF ANGLES Straight Angles Angles which measure exactly…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,123],"tags":[],"class_list":["post-1287","post","type-post","status-publish","format-standard","hentry","category-posts","category-third-term-jss2-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=1287"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1287\/revisions"}],"predecessor-version":[{"id":1288,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/1287\/revisions\/1288"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=1287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=1287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=1287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}