In the adjoining 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.
Let us mark the points A and B on p; X and Y on q; P and Q on l; R and S on m.
Suppose AB and XY intersect PQ at K and L respectively.
Suppose AB and XY intersect RS at N and M respectively.
Since, p||q and l is a transversal, then
m∠AKL + m∠XLK = 180° (Interior angles on same side of transversal are supplementary)
⇒ 80° + m∠XLK = 180°
⇒ m∠XLK = 180° − 80°
⇒ m∠XLK = 100°
Since, PQ and XY are straight lines that intersect at L, then
m∠QLM = m∠XLK (Vertically opposite angles)
⇒ a = 100°
Since, l||m and p is a transversal, then
m∠BNR = m∠AKL (Alternate exterior angles)
⇒ c = 80°
Since, p||q and m is a transversal, then
m∠NMY= m∠RNB (Corresponding angles)
⇒ b = c
⇒ b = 80°