# 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 = 70o, 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 = 65o and ∠C = 45o in ∆ ABC and DAE ∥ BC. If ∠DAB = xo and ∠EAC = yo, find the values of x and y. (6) In the adjoining figure, it is given that CE ∥ BA, ∠BAC = 80o and ∠ECD = 35o. Find = (i) ∠ACE, (ii) ∠ACB, (iii) ∠ABC (7) In the adjoining figure, it is being given that AO ∥ CD, OB ∥ CE and ∠AOB = 50o. Find the measure of ∠ECD. (8) In the adjoining figure, it is given that AB ∥ CD, ∠ABO = 50o and ∠CDO = 40o. 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 = 120o, ∠ECD = 100o and ∠BEC = xoFind 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 = 35o, ∠CAD = 40o, ∠ACB = xo and ∠ACD = yo, find the values of x and y. (14) In the given figure, AB ∥ CD and CA has been produced to E so that ∠BAE = 125o. If ∠BAC = xo, ∠ABD = xo, ∠BDC = yo and ∠ACD = zo, 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. Updated: May 30, 2022 — 1:34 pm

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