{"id":5350,"date":"2023-02-16T10:33:09","date_gmt":"2023-02-16T05:03:09","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=5350"},"modified":"2023-03-30T10:34:40","modified_gmt":"2023-03-30T05:04:40","slug":"ap-board-9th-class-maths-solutions-chapter-4-intext-questions","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/ap-board-9th-class-maths-solutions-chapter-4-intext-questions\/","title":{"rendered":"AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions"},"content":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions<\/a> Chapter 4 Lines and Angles InText Questions and Answers.<\/p>\n

AP State Syllabus 9th Class Maths Solutions 4th Lesson Lines and Angles InText Questions<\/h2>\n

Question
\nObserve your surroundings carefully and write any three situations of your daily life where you can observe lines and angles. [Page No. 71]
\nSolution:
\nThe edges of a blackboard; the edges of a ruler\/scale and the edges of a table gives the idea of lines and their corners give the idea of angles.<\/p>\n

Question
\nDraw the pictures in your notebook and collect some pictures. [Page No. 71]
\nSolution:
\n\"AP<\/p>\n

Think, Discuss and Write<\/strong><\/p>\n

What is the difference between inter-secting lines and concurrent lines ? [Page No. 74]
\nSolution:
\nIf the number of lines meeting at a point are only two then they are said to be intersecting lines whereas if the lines are three or more than three meeting at a point then they are said to be concurrent lines.
\n\"AP<\/p>\n

Do These<\/strong><\/p>\n

Question 1.
\nWrite the complementary, supplementary and conjugate angles for the following angles, a) 45\u00b0 b) 75\u00b0 c) 215\u00b0 d) 30\u00b0 e) 60\u00b0 f) 90\u00b0 g) 180\u00b0 [Page No. 76]
\nSolution:
\n\"AP<\/p>\n

Question 2.
\nWhich pairs of the following angles become complementary or supplementary. [Page No. 76]
\n\"AP
\nSolution:
\nThe angles formed by the figures (i) and (ii) are complementary.
\nThe angles formed by the figures (ii) and (iii) are supplementary.<\/p>\n

\"AP<\/p>\n

Try This<\/strong><\/p>\n

Question 1.
\nFind the pairs of adjacent and non- adjacent angles in the given figures. [Page No. 77]
\n\"AP
\nSolution:
\nIn figure (i) \u22201 and \u22202 are pair of adjacent angles.
\nIn figure (ii), no adjacent angles.
\nIn figure (iii) (\u22201, \u22202), (\u22202, \u22203) are pairs of adjacent angles.
\nIn figure (iv) \u22201 and Z2 are adjacent angles.<\/p>\n

ii) List the adjacent angles in the given figure. [Page No. 77]
\n\"AP
\nSolution:
\nIn the given figure
\n(\u22201, \u22202), (\u22203, \u22204), (\u22204,\u22205) and (\u22203, \u22205) are the pairs of adjacent angles.<\/p>\n

\"AP<\/p>\n

Think Discuss and Write<\/strong><\/p>\n

Question
\nLinear pair of angles are always supplementary. But supplementary angles need not form a linear pair. Why ? [Page No. 77]
\nSolution:
\nA pair of supplementary angles need not necessarily a linear pair because they may exists in separate figures.<\/p>\n

Activity<\/strong><\/p>\n

Measure the angles in the following figure and complete the table.
\n[Page No. 78]
\n\"AP
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Measure the four angles 1,2,3,4 in each of the above figure and complete the table:
\n[Page No. 79]
\n\"AP
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Do This<\/strong><\/p>\n

Question 1.
\nClassify the given angles as pairs of complementary, linear pair, vertically opposite and adjacent angles. [Page No. 80]
\n\"AP
\nSolution:
\nThe pairs of angles a and b in the fig.(i) are linear pair of angles.
\nThe pairs of angles a and b in the fig.(ii) are adjacent angles.
\nThe pairs of angles a and b in the fig.(iii) are complementary angles*
\nThe pairs of angles a and b in the fig.(iv) are vertically opposite angles.<\/p>\n

Question 2.
\nFind the measure of angle ‘a’ in each figure. Give reasons in each case. [Page No. 81]
\ni)
\n\"AP
\na = 180\u00b0 – 50\u00b0 = 130\u00b0
\n(linear pair of angles)<\/p>\n

\"AP<\/p>\n

ii)
\n\"AP
\na = 43\u00b0
\n( \u2235 vertically opposite angles)<\/p>\n

iii)
\n\"AP
\na = 360\u00b0 – (209\u00b0 + 96\u00b0)
\n= 360\u00b0 – 305\u00b0 = 55\u00b0
\n(\u2235 complete angle = 360\u00b0)<\/p>\n

iv)
\n\"AP
\na = 90\u00b0 – 63\u00b0 = 27\u00b0
\n(pair of complementary angles )<\/p>\n

\"AP<\/p>\n

Do These<\/strong><\/p>\n

Question 1.
\nFind the measure of each angle indi-cated in each figure where \/ and m are parallel lines intersected by a transversal n. [Page No. 87]
\n\"AP
\nSolution:
\nx = 110\u00b0 (alternate exterior angles)<\/p>\n

\"AP<\/p>\n

\"AP
\nSolution:
\ny = 84\u00b0 (alternate interior angles)<\/p>\n

\"AP
\nSolution:
\nz = 180\u00b0 – 100\u00b0 = 80\u00b0 .
\n(interior angles on the same side of transversal)<\/p>\n

\"AP
\nSolution:
\ns\u00b0 = 53\u00b0 (pair of corresponding angles)<\/p>\n

\"AP<\/p>\n

Question 2.
\nSolve for x and give reasons. [Page No. 88]
\n\"AP
\n11x + 2 = 75\u00b0
\n11x = 75 – 2 = 73
\n\u2234 x = \\(\\frac{73}{11}\\)
\n(\u2234 pair of corresponding angles are equal).<\/p>\n

\"AP
\nSolution:
\n8x – 4 = 60\u00b0
\n8x = 60 + 4 = 64
\n\u2234 x = \\(\\frac{64}{8}\\) = 8
\n(\u2234 alternate interior angles are equal)<\/p>\n

\"AP
\nSolution:
\n(14x- 1)\u00b0.= (12x + 17)\u00b0
\n14x – 12x = 17 + 1
\n2x = 18
\nx = \\(\\frac{18}{2}\\) = 9
\n(\u2234 alternate exterior angles are equal)<\/p>\n

\"AP
\nSolution:
\n13x- 5 = 17x + 5
\n13x- 17x = 5 + 5
\n– 4x = 10
\nx = \\(\\frac{10}{-4}=\\frac{-5}{2}\\)
\n(\u2234 Pair of, corresponding angles are equal).<\/p>\n

\"AP<\/p>\n

Activity<\/strong><\/p>\n

Question 1.
\nTake a scale and a ‘set sqaure’. Arrange the set sqare on the scale as shown in figure. Along the slant edge of set sqare draw a line with the pencil. Now slide your set square along its horizontal edge and again draw a line. We observe that the lines are parallel. Why are they parallel ? Think and discuss with your friends. [Page No. 88]
\nSolution:
\n\"AP<\/p>\n

A. Student Activity (For Reference .)
\nAll slant lines are parallel making an angle of 60\u00b0 with the horizontal line. In this figure horizontal line is transversal to the slant line and corresponding angles are equal.<\/p>\n

Do This<\/strong><\/p>\n

Question
\nDraw a line \\(\\overline{\\mathbf{A D}}\\) and mark points B and C on it. At B and C, construct \u2220ABQ and \u2220BCS equal to each other as shown. Produce QB and SC on the other side of AD to form two lines PQ and RS.<\/p>\n

Draw common perpendiculars EF and GH for the two lines PQ and RS. Measure the lengths of EF and GH. What do you observe ? What can you conclude from that ? Recall that if the perpendicular distance between two lines is the same, then they are parallel lines. [Page No. 89]
\n\"AP
\n\"AP
\nSolution:
\nAs \u2220ABQ =\u2220BCS and they lie on the same line AD we can say that BQ \/\/ CS. Now EF and GH are the perpendicular distances between two parallel lines PQ and R, we say EF = GH.<\/p>\n

\"AP<\/p>\n

Try This<\/strong><\/p>\n

Question i)
\nFind the measure of the question marked angle in the given figure. [Page No. 90]
\n\"AP
\nSolution:
\n? = 70\u00b0
\n[ \u2235 from the figure, these two angles are exterior angles on the same side of the transversal]<\/p>\n

ii) Find the angles which are equal to \u2220P.
\nSolution:
\n\u2220P = \u2220Q = \u2220R = 110\u00b0
\n(corresponding angles)<\/p>\n

Activity<\/strong><\/p>\n

Question
\nDraw and cut out a large triangle as shown in the figure.
\nNumber the angles and tear them off.
\nPlace the three angles adjacent to each other to form one angle as shown below. [Page No. 97]
\n\"AP
\n1. Identify angle formed by the three adjacent angles ? What is its mea-sure ?
\n2. Write about the sum of the measures of the angles of a triangle. Now let us prove this statement
\nusing the axioms; and theorems related to parallel lines.
\nSolution:
\nStudent Activity.<\/p>\n

\"AP<\/p>\n

Think, Discuss and Write<\/strong><\/p>\n

Question
\nIf the sides of a triangle are produced in order, what will be the sum of exterion angles formed ? [Page No. 99]
\nSolution:
\nLet \u0394ABC and the sides of the triangle is formed by exterior angles.
\n\"AP
\n\u22203 = \u2220B + \u2220C
\n\u22201 + \u22202 + Z\u22203 = 2[\u2220A + \u2220B + \u2220C]
\n= 2 x 180\u00b0 = 360\u00b0
\n\u2234 Sum of the exterior angles are 360\u00b0.<\/p>\n

AP Board 9th Class Maths Solutions<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus\u00a0AP Board 9th Class Maths Solutions Chapter 4 Lines and Angles InText Questions and Answers. AP State Syllabus 9th Class Maths Solutions 4th Lesson Lines and Angles InText Questions Question Observe your surroundings carefully and write any three situations of your daily life where you can observe lines and angles. [Page No. 71] … Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":36010,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/apboardsolutions.com\/wp-content\/uploads\/2023\/02\/Chapter-4-Lines-and-Angles-InText-Questions.png","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/5350"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=5350"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/5350\/revisions"}],"predecessor-version":[{"id":34242,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/5350\/revisions\/34242"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media\/36010"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=5350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=5350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=5350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}