If you add two acute angles in which each angle is large as possible, its sum will be less than 180°. PLAY. 100. Complementary angles must be acute. Solution: Question 9. Angles /_1 and /_2 are adjacent (share one side) and acute. (iii) Two obtuse angles can form a linear pair. A pair of vertical angles can be complementary. Books; Test Prep; Summer Camps; Office Hours; Earn Money ; Log in ; Join for Free. (xii) Corresponding angles are on the ……….. side of the transversal. (b) obtuse (viii) Angles formed by two intersecting lines having no common arms are called vertically opposite angles. Solution: Question 13. Question 61. A pair of complementary angles is (a) 130°, 50° (b) 35°, 55° (c) 25°, 75° (d) 27°, 53° Solution: A pair of complementary angles is 35°, 55°. (ii) Two acute angles can form a linear pair. (iii) ∠AOC is ………… of ∠COD. (b) x = 60 Otherwise, these angles are different. Space is limited so join now!View Summer Courses. (iii) Two obtuse angles can form a linear pair. (xi) Alternate interior angles have one common arm. If lines are parallel than the corresponding angle are the same and if lines are not parallel than angles are different. Then the values of x and y are respectively: (a) 50°, 120° (b) 50°, 130° (c) 60°, 120° (d) 60°, 130° Solution: In the given figure, PA || BC || DQ AB || DC x = 50° (Alternate angles) ∠BCD + ∠ABC = 180° (Sum of co-interior angles) ⇒ ∠DCB + 50° = 180° ⇒ ∠DCB = 180° – 50° = 130° BC || DQ ∠DCB = ∠CDQ (Alternate angles) y = 130° x = 50°, y = 130° (b), Question 1. If an angle measures 10° more than its complement, then the measure of the angle is Ans : False 2. (vi) Angles of a linear pair are as well as ……….. , Two acute angles can be supplementary. If a transversal intersects two parallel lines, then each pair of alternate interior angles are equal. (d) x = 115° A pair of complementary angles is (v) Pair of vertically opposite angles are always supplementary. Ans : True 3. As the sum of supplementary angles is 180°. 3.adjacent supplementary angles form a linear pair. (vii) If two lines are cut by a transversal, Learn. find the measure of a supplement of /_2. Solution: Choose the correct answer from the given four options (4 to 14): (xiv) If two lines are cut by a transversal such that a pair of corresponding angles are not equal, then the lines are ……….. Fill in the blanks: (i) If two angles are complementary, then the sum of their measures is ……….. (ii) If two angles are supplementary, then the sum of their measures is ………… (iii) Supplement of an obtuse angle is ………. (viii) If two lines are cut by a transversal, then each pair of alternate interior angles are equal. Two right angles can be supplementary Get the answers you need, now! A pair of vertical angles can be supplementary. (ii) ∠AOC and ∠COB are ……….. angles. Solution: Question 1. Find the value of x in each figure. sophiasolan. Calculate the measure of each lettered angle in the following figures (parallel line segments / rays are denoted by thick matching arrows): Solution: (i) In the given figure, Given ∠s are 72° and 55° a = 55° (Corresponsing angles) c = 72° (Alternate angles) But b + c + 55° = 180° (Angles on the one side of a straight line) ⇒ b + 72° + 55° = 180° ⇒ b + 127° = 180° ⇒ b = 180° – 127° = 53° a = 55, b = 53°, c = 72° (ii) In the given figure, Given ∠s are 135° and 110° p = 135° (Alternate angles) p + r + 110° = 360° (Angles at a point) ⇒ 135° + 110° + r = 360° ⇒ 245° + r = 360° ⇒ r = 360° – 245° = 115° But r + q = 180° (Co-interior angles) ⇒ 115° + q = 180° ⇒ q = 180° – 115° = 65° p = 135°, q = 65°, r = 115° (iii) In the given figure, Given angle is 110° p = ∠1 (Vertically opposite angles) But ∠1 + 110° = 180° (Co-interior angles) ⇒ ∠1 = 180° – 110° = 70° ⇒ p = ∠1 = 70° s = 110° (Alternate angles with 110°) p = q (Corresponding angles) q = 70° r = q (Alternate angles) r = 70° Now, p = 70°, q = 70°, r = 70°, s = 110°, ICSE Previous Year Question Papers Class 10, ML Aggarwal Class 7 Solutions for ICSE Maths, Concise Mathematics Class 10 ICSE Solutions, Concise Chemistry Class 10 ICSE Solutions, Concise Mathematics Class 9 ICSE Solutions, Thank You Letter for Job Interview, Friend, Boss, Support | Appreciation and Format of Thank You Letter, How To Write a Cover Letter | Format, Sample and Important Guidelines of Cover letter, How to Address a Letter | Format and Sample of Addressing a Letter, Essay Topics for High School Students | Topics and Ideas of Essay for High School Students, Model Essay for UPSC | Tips and List of Essay Topics for UPSC Exam, Essay Books for UPSC | Some Popular Books for UPSC Exam, Sample Essay for UPSC | How to Prepare and Important Essay Topics for UPSC Exam, IAS Essay Topics | Important List of IAS Essay Topics for Students and Children in English, CAPF Essay Topics | Important Topics of CAPF Essay for Students and Children in English, Value of Games Essay | Essay on Value of Games for Students and Children in English, Bullying in Schools Essay | Essay on Bullying in Schools for Students and Children in English. There are 3 interior angles in a triangle; therefore no two angles in a triangle can ever be supplemental whether it is a right triangle or not. (x) Two lines in a plane which never meet are called ………. How To Find The Area Of A Triangle, Given Only Two Angles And One Side? (iv) Two adjacent angles always form a linear pair. By definition, supplementary angles add up to 180° therefore they are linear pairs, if they are adjacent. (ii) Two acute angles can form a linear pair. In the given figure, PA || BC || DQ and AB || DC. (ii) Two acute angles can form a linear pair. Acute angles are those which are less than 90°. Gravity. Fill in the blanks: (c) 3 (b) 55° Your email address will not be published. Solution: Question 2. (xiv) If two lines are cut by a transversal such that a pair of corresponding angles are not equal, then the lines are not parallel. (d) 40°, 50° (ii) Two acute angles can form a linear pair. The measure of the complement of the angle 46° is (a) 90° (b) 46° (c) 16° … true. (False) Correct: As the sum of two adjacent angles can be less than 180° or more than 180°. The Sum Of The Measure Of The First Angle And Half The Second Angle Is 80.5%. TRUE/FALSE DIRECTION : Read the following statements and write your answer as true or false. Vertical angles must have the same measure. Calculate the measure of each lettered angle in the following figures (parallel line segments / rays are denoted by thick matching arrows): AB || CD ∠APQ = ∠PQR (Alternate angles) ∠PQR = 50° ∠PRD + ∠PRQ = 180° (Linear pair) 130° + ∠PRQ = 180° ∠PRQ = 180° – 130° = 50° Now in ∆PQR ∠PQR + ∠PRQ + ∠QPR = 180° (Angles of a triangle) 50° + 50° + ∠QPR = 180° ∠QPR = 180° – 50° – 50° = 80° (c), Question 14. true or false 1.vertically opposite angles are always supplementary. If false give a counterexample. FALSE. If two angles are acute, then they are supplementary. Solution: Question 10. False - 2 acute angles do not add to 180 degrees . (iii) Two obtuse angles can form a linear pair. (iv) Two adjacent angles always form a linear pair. In the given figure, the value of x that will make AOB a straight line is (a) x = 40 (b) x = 35 (c) x = 30 (d) x = 25 Solution: AOB will be a straight line if 3x + 15 + 2x – 10° = 180° ⇒ 5x + 5 = 180° ⇒ 5x = 180° – 5 = 175° ⇒ x = 35° (b), Question 10. Write. (c) x = 105° As one acute angle and one obtuse angle can make two supplementary angles. (vi) 30° is one-half of its complement. (vi) 30° is one-half of its complement. A pair of acute angles can be supplementary. Verticle angles never have equal measure. Solution: Question 12. (c) x = 30 (d) straight true. true or false: Q is the vertex of Angles- > solution: ( i ) if two angles and one.... Be parallel since that is a straight line and OD ⊥ AB: if two lines cut... Arm, and No common interior points in a plane which never meet are called vertically opposite angles the... 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