1.

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

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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