Question

18. Case Study based-2Types of angles and angle sum property of a triangleIt is 7:00 am!Shikha rolls out her yoga mat and starts her warm up session with stretching andbending. Anaya her daughter is sitting nearby, observing her mother's daily ritualAnaya takes a picture of her mother while she was in a yoga posture and label it asshown.22-15(a) Angles ZLKM and ZJKL are called as?Linear Pair of angles(11) Vertically opposite angles(iii) Complementary angles(iv) Corresponding angles(b) Find m2LKM.(1)195° -x(in) 185°- 2x(it) 1950 - 2x(iv) 185° - *(C) Find mZKLM.0115°(i) 65°(ii) 50°(iv) 180°(d) Which of the following is true for ALKM?(1) ALKM is an equilateral triangle.(11) ALKM is an isosceles triangle.(ill) ALKM is a right angle triangle(iv) All of the above(e) What is the measurement of the ZLKJ?(1) 115°

Answer 1

(a) Angles ∠LKM and ∠JKL are called as ?

(i) Linear Pair of angles (ii) Vertically opposite angles

(iii) Complementary angles (iv) Corresponding angles .

Answer :-

→ ∠LKM + ∠JKL = 180° (Linear pair of angles. since JM is a straight line.)

so, Option (i) is correct answer .

(b) Find ∠LKM ?

(i)195° -x (ii) 185°- 2x (iii) 195 - 2x (iv) 185° - x

Answer :-

→ ∠LKM + ∠JKL = 180° (Linear pair of angles)

→ ∠LKM + (2x - 15)° = 180°

→ ∠LKM = 180° - (2x - 15)°

→ ∠LKM = 180° + 15° - 2x

→ ∠LKM = (195 - 2x)° (option iii)

(C) Find ∠KLM ?

(i)115° (ii) 65° (iii) 50° (iv) 180°

Answer :-

In ∆KLM , we have,

→ ∠KLM + ∠LMK = ∠JKL { Exterior angle is equal to sum of interior opposite angles. }

→ x° + 50° = (2x - 15)°

→ 50° + 15° = 2x - x

→ x = 65° (option ii)

(d) Which of the following is true for ∆LKM ?

(i) ALKM is an equilateral triangle. (ii) ALKM is an isosceles triangle . (iii) ALKM is a right angle triangle (iv) All of the above

Answer :-

In ∆LKM , we have,

→ ∠LMK = 50°

→ ∠KLM = 65°

so,

→ ∠KLM + ∠LMK + ∠LKM = 180° (By angle sum property.)

→ 65° + 50° + ∠LKM = 180°

→ 115° + ∠LKM = 180°

→ ∠LKM = 180° - 115°

→ ∠LKM = 65° .

since,

→ ∠LKM = ∠KLM = 65°

→ KM = ML (opposite sides of equal ∆ are equal.)

therefore, (ii) ∆LKM is an isosceles triangle .

(e) What is the measurement of the ∠LKJ ?

(i) 115° (ii) 65° (iii) 50° (iv) 180° .

Answer :-

→ ∠LKJ = (2x - 15)°

→ ∠LKJ = (2*65 - 15)°

→ ∠LKJ = (130 - 15)°

→ ∠LKJ = 115° option (i)

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