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).

Answer 1

(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.