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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.

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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°

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