## 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.**

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