5) In the following figure lines 1 || m and p || q, find a, b, c and d:
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line l|| line m and line p is a transversal.
∴ m∠a = 78° …
(i) [Corresponding angles] ii. line p || line q and line m is a transversal.
∴ m∠d = m∠a …[Corresponding angles]
∴ m∠d = 78° …
(ii) [From (i)] iii. m∠b = m∠d …[Vertically opposite angles]
∴ m∠b = 78° …
[From (ii)] iv. line l|| line m and line q is a transversal.
∴ m∠c + m∠d = 180° …[Interior angles]
∴ m∠c + 78° = 180° …
[From (ii)]
∴ m∠c =180° – 78°
∴ m∠c = 102°
∴ m∠a = 78°, m∠b = 78°, m∠c = 102°, m∠d = 78°
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