Rs Aggarwal 2017 Solutions for Class 7 Math Chapter 14 Properties Of Parallel Lines are provided here with simple step-by-step explanations. These solutions for Properties Of Parallel Lines are extremely popular among Class 7 students for Math Properties Of Parallel Lines Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 7 Math Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 177:

Question 1:

In the given figure, l || m and t is a transversal.
If ∠5 = 70°, find the measure of each of the angles
∠1, ∠3, ∠4 and ∠8.

Answer:

Given: lmt is a transversal.5 = 70° 5 = 3  =70°    (alternate interior angles)5 +8 = 180°   (linear pair)or 70° + 8 = 180°8 = 110°1 = 3 = 70°   (vertically opposite angles)3 +4 = 180°   (linear pair)or 4 = 180-3 = 180 - 70 = 110°



Page No 178:

Question 2:

In the given figure, l || m and t is a transversal. If ∠1 and ∠2 are in the ratio 5 : 7, find the measure of each of the angles
∠1, ∠2, ∠3 and ∠8.

Answer:



Given: lmt is a transversal.1:2 = 5:7Let the angles measure 5x and 7x.  1+2 = 180°                   (linear pair) 5x + 7x = 180                   or 12x = 180or x = 15 1 = 5x = 5(15) = 75°and 2 = 7x = 7(15) = 105° 2+3 = 180°                 (linear pair)3 = 180-105 = 75°3+6 = 180                     (interior angles on the same side of the transversal are supplementary)6 = 180-3 = 105°and 6 =8 =105°            (vertically opposite angles) 1 = 75°      2 = 105°      3 = 75°      8 = 105° 

Page No 178:

Question 3:

Two parallel lines l and m cut by a transversal t. If the interior angles of the same side of t be (2x − 8)° and (3x − 7)°, find the measure of each of these angles.

Answer:

Given: lmt is a transversal.Let: 1 =(2x-8)°2 = (3x-7)°We know that the consecutive interior angles are supplementary. 1 +2 =180°or  (2x-8) + (3x-7) =180or 5x -15 = 180or 5x = 195or x = 391 = (2x-8) = (2×39-8) = 70°2  =(3x-7) = (3×39-7) = 110°

Page No 178:

Question 4:

In the given figure, l || m. If s and t be transversals such that s is not parallel to t. find the values of x and y.

Answer:

From the given figure:

 1 =3 = 50° (corresponding angles)and  1 + x° = 180° (linear pair)or x°  = 180° - 50° = 130°or x = 130 2 =4 = 65° (corresponding angles)and  2 + y° = 180° (linear pair)or y° = 180° - 65° =115°or y= 115

Page No 178:

Question 5:

In the given figure, ∠B = 65° and ∠C = 45° in ∆ABC and DAE || BC. If ∠DAB = x° and ∠EAC = y°, find the values of x and y.

Answer:

Given: B = 65°C = 45°DAE BC The given lines are parallel.  x° = B = 65°      (alternate angles when AB is taken as the transversal) y° = C =45°             (alternate angles when AC is taken as the transversal) x = 65 y  =45

Page No 178:

Question 6:

In the adjoining figure, it is given that CE || BA, ∠BAC = 80° and ∠ECD = 35°.
Find (i) ∠ACE, (ii) ∠ACB,  (iii) ∠ABC.

Answer:

Given: CE BA BAC= 80°, ECD = 35°(i) BAC = ACE = 80°      (alternate angles with AC as a transversal)(ii) ACB + ACD = 180°    (linear pair)or ACB + ACE + ECD = 180°orACB + 80°+35° =180°or ACB = 65°(iii) In ABC: BAC + ACB +ABC = 180°   (angle sum property)80° +65° + ABC  = 180°ABC  = 35°

Page No 178:

Question 7:

In the adjoining figure, it is being given that AO || CD, OB || CE and ∠AOB = 50°
Find the measure of ∠ECD.

Answer:

Given: AO CD             OB CE            AOB = 50°AOD = CDB = 50°              (when  AO CD and OB is the transversal)ECD +CDB = 180°             (consecutive interior angles are supplementary, DB CE and CD is the transversal)ECD = 180°-50° = 130°

Page No 178:

Question 8:

In the adjoining figure, it is given that AB || CD,AOB = 50° and ∠CDO = 40°.
Find the measure of ∠BOD.

Answer:

Given: ABCD            ABO = 50°            CDO = 40°Construction: Through O, draw EOFAB.ABO = BOF = 50°            (alternate angles, when ABEF and OB is a transversal)FOD = ODC = 40°          (alternate angles, when CDEF and OD is a transversal) BOD = BOF  + FODBOD = 50°+40° =90°

Page No 178:

Question 9:

In the given figure, AB || CD and a transversal EF cuts them at G and H respectively.
If GL and HM are the bisectors of the alternate angles ∠AGH and ∠GHD respectively, prove that GL || HM.

Answer:

Given: AB CD              GL and HM are angle bisectors of AGH and GHD, respectively. AGH=GHD (alternate angles)or 12 AGH=12GHDor LGH = GHM    (given)Therefore, GL  HM as we know that if the angles of any pair of alternate interior angles are equal, then the lines are parallel. 



Page No 179:

Question 10:

In the given figure, AB || CD,
ABE = 120°, ∠ECD = 100° and ∠BEC = x°
Find the value of x.

Answer:

Given: AB CD            ABE = 120°           ECD = 100°           BEC = x°Construction: FEG ABNow, since ABFEG and ABCD, FEGCD EFGABCDABE = BEG = 120° (alternate angles)or x°+y° = 120°  ....(i)DCE = CEF = 100°   (alternate angles)or x°+z° = 100°   .....(ii)Also, x°+y°+z° = 180°       (FEG is a straight line)   ...(iii)Adding (i) and (ii):2x°+y°+z° = 220°or, x° +180° = 220° (substituting (iii))x° = 40° x = 40

Page No 179:

Question 11:

In the given figure, ABCD is a quadrilateral in which AB || DC and AD || BC.
Prove that ∠ADC = ∠ABC.

Answer:

Given: AB CD            AD BC1 + 2 = 180°            (ABCD and AD is the transversal)    ...(i)2+ 3 =180°              (ADBC and AB is the transversal)    ...(ii)From (i) and (ii):1 + 2 = 180° = 2+ 3 1 = 3ADC = ABC

Page No 179:

Question 12:

In the given figure, l || m and p || q.
Find the measure of each of the angles ∠a, ∠b, ∠c and ∠d.

Answer:

Given: lm pq 1 = 65°1 = a =  65°         (vertically opposite angles)a + d = 180°            (consecutive interior angles on the same side of a transversal are supplementary)or d = 180°-65°= 115°c+ d = 180°              (consecutive interior angles on the same side of a transversal are supplementary)or c = 180°-115°= 65°c+ b = 180°               (consecutive interior angles on the same side of a transversal are supplementary)or b = 180°-65°= 115° a = 65°b = 115°c= 65°d= 115°

Page No 179:

Question 13:

In the given figure, AB || DC and AD || BC, and AC is a diagonal. If ∠BAC = 35°, ∠CAD = 40°, ∠ACB = x° and ∠ACD = y°, find the value of x and y

Answer:

Given: AB DCADBCBAC = 35°CAD =40° BAC = y=  35°              (alternate angles when ABDC)CAD = x = 40°                  (alternate angles when ADBC)  x = 40 y=  35

Page No 179:

Question 14:

In the given figure, AB || CD and CA has been produced to E so that ∠BAE = 125°.
If ∠BAC = x°, ∠ABD = x°, ∠BDC = y° and ∠ACD = z°, find the values of x, y, z.

Answer:

Given: AB CD BAE = 125°CAB + BAE  =180°or 125° + x°= 180°or x = 55x + z =180° (consecutive interior angles on the same side of transversal are supplementary)z =180-x = 180 -55 = 125y + x =180° (consecutive interior angles on the same side of transversal are supplementary)y  =180- x = 180- 55 =  125

Page No 179:

Question 15:

In each of the given figures, two lines l and m are cut by a transevrsal t.
Find whether l || m.

Answer:

(i) 1+2 = 180 (linear pair)or 130° + 2 = 180°or 2 = 50° 40° =3 lm(ii) 2+3 = 180° (linear pair)35°+3 = 180°3 = 145°= 145° = 1  lm(iii)2+3 = 180 (linear pair)3 =180°- 125° = 55°3 =55° 60° = 1 lm







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