In the given figure, line p || line q, line l || line m. Find measures

1.	In the given figure, line p \|\| line q, line l \|\| line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.
Answer» i. line p \|\| line q and line l is a transversal. ∴ m∠a + 80° = 180° …[Interior angles] ∴ m∠a= 180° – 80° ∴ m∠a= 100° ii. line l \|\| line m and line p is a transversal. ∴ m∠c = 80° …(i) [Exterior alternate angles] iii. line p \|\| line q and line m is a transversal. ∴ m∠b = m∠c … [Corresponding angles] m∠b = 80° …[From (i)] ∴ m∠a = 100°, m∠b = 80°, m∠c = 80°

In the given figure, line p || line q, line l || line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Answer»

i. line p || line q and line l is a transversal.

∴ m∠a + 80° = 180° …[Interior angles]

∴ m∠a= 180° – 80°

∴ m∠a= 100°

ii. line l || line m and line p is a transversal.

∴ m∠c = 80° …(i) [Exterior alternate angles]

iii. line p || line q and line m is a transversal.

∴ m∠b = m∠c … [Corresponding angles]

m∠b = 80° …[From (i)]

∴ m∠a = 100°, m∠b = 80°, m∠c = 80°