RS Aggarwal Class 7 Math Fourteenth Chapter Properties of Parallel Lines Exercise 14 Solution

RS Aggarwal Class 7 Math Fourteenth Chapter Properties of Parallel Lines Exercise 14 Solution

EXERCISE 14

(1) In the given figure, l ∥ m and t is a transversal. If ∠5 = 70^o, find the measure of each of the angles ∠1, ∠3, ∠4 and ∠8.

(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.

(3) Two parallel lines l and m are cut by a transversal t. If the interior angles of the same side of t be (2x – 8)^o and (3x – 7)^o, find the value of x and y.

(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.

(5) In the given figure, ∠B = 65^o and ∠C = 45^o in ∆ ABC and DAE ∥ BC. If ∠DAB = x^o and ∠EAC = y^o, find the values of x and y.

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

(7) In the adjoining figure, it is being given that AO ∥ CD, OB ∥ CE and ∠AOB = 50^o. Find the measure of ∠ECD.

(8) In the adjoining figure, it is given that AB ∥ CD, ∠ABO = 50^o and ∠CDO = 40^o. Find the measure of ∠BOD.

(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.

(10) In the given figure, AB ∥ CD, ∠ABE = 120^o, ∠ECD = 100^o and ∠BEC = x^o. Find the value of x.

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

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

(13) In the given figure, AB ∥ DC and AD ∥ BC, and AC is a diagonal. IF ∠BAC = 35^o, ∠CAD = 40^o, ∠ACB = x^o and ∠ACD = y^o, find the values of x and y.

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

(15) In each of the given figures, two lines l and m are cut by a transversal t. Find whether l ∥ m.