#### Question

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.

#### Solution

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°