Question

# In Fig. 15.17, line n is a transversal to lines l and m. Identify the following (i) Alternate and corresponding angles in Fig. 15.17 (i). (ii) Angles alternate of ∠d and ∠g and angles corresponding to angles ∠f and ∠h in Fig. 15.17 (ii). (iii) Angle alternative to ∠PQR, angle corresponding to ∠RQF and angle alternate to ∠PQE in Fig. 15.17 (iii). (iv) Pairs of interior and exterior angles on the same side of the transversal in Fig. 15.17 (ii).

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Solution

## (i) Alternate Interior angles are: ∠BGH and ∠CHG, ∠ AGH and ∠DHG ​ Alternate Exterior angles are: ∠AGE and ∠DHF, ∠ EGB and ∠CHF Corresponding angles are: ​∠EGB and ​∠GHD, ​∠EGA and ​∠GHC, ​∠BGH and ​∠DHF, ​∠AGH and ​∠CHF (ii) The alternate angle to ∠d is ∠​e and alternate angle to ∠g is ∠​b. The corresponding angles to ∠​f is ∠​c and ∠h is∠​a. (iii) In the given figure, 'l' is a transversal line to 'm' and 'n'. So, the alternate angle of ∠​ PQR is ∠ QRA. The corresponding angle of ∠​ RQF is ∠BRA. The alternate angle of ∠​PQE is∠BRA. (iv) Interior angles on the same side of the transversal line 'n' are: ∠d and ∠ f, ∠a and ∠e. Exterior angles on the same side of the transversal line 'n' are: ∠c and ∠g, ∠​b and ∠​h.

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