Question

In the figure, given that ∥ and t is a transversal. If ∠ 1 = (110° – ) and ∠5 = 4, then
the measures of ∠ 1 and ∠ 5 are∶
(a) 55°, 55° (b) 22°, 88° (c) 55°, 88° (d) 88°, 88°

Answer 1

Step-by-step explanation:

Two parallel lines l and m be cut by a transversal t, forming angles. It is given that ∠5 = 70°. Now, ∠5 = ∠3 = 70° … [∵ alternate interior angles] ∠5 + ∠8 = 180° … [∵ linear pair] 70° + ∠8 = 180° ∠8 = 180° – 70 ∠8 = 110° ∠1 = ∠3= 70° … [∵ vertically opposite angles] ∠3 + ∠4 = 180° … [∵ linear pair] 70 + ∠4 = 180° ∠4 = 180° – 70° ∠4 = 110° ∴ ∠1 = 70°, ∠3 = 70°, ∠4 = 110° and ∠8 = 110°.