Question

5. In the given figure, 21 = 120°.
Calculate the degree measure of
2, 3, 4, 5, 6, 7 and 8.
Give reasons.























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Answer 1

Answer:

∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°.

Step-by-step explanation:

∥ m and p is their transversal and ∠1 = 120°

∠1 + ∠2 = 180° (Straight line angle)

∴ 120° + ∠2 = 180° ⇒ ∠2 = 180° – 120° = 60°

∠2 = 60°

But ∠1 = ∠3 (Vertically opposite angles)

∴ ∠3 = ∠1 = 120°

Similarly ∠4 = ∠2 (Vertically opposite angles)

∠4 = 60°

∠5 = ∠1 (Corresponding angles)

∠5 = 120°

Similarly ∠6 = ∠2 (Corresponding angles)

∴ ∠6 = 60°

∠7 = ∠5 (Vertically opposite angles)

∠7 = 120°

and ∠8 = 60° (vertically opposite angles)

Hence ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°.