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In the figure, line l || line m and line p || line q. Find the measures of ∠a, ∠b, ∠c and ∠d. |
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Answer» i. 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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