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.

Answer 1

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°