Question

Do not assume that any of the angles are equal. Show your work.

1. if ∠ 3 is 45 degrees. Find ∠9.
2. if ∠2 = 72 degrees, and ∠4 = 57 degrees, find ∠3.
3. if ∠7 = 120 degrees, and ∠5 = 40 degrees. Find ∠1.
4. if ∠8 = 145 degrees, and ∠1 = 37 degrees, find ∠2.
5. if ∠2 = 72 degrees, and ∠4 = 57 degrees, find ∠3.
6. ∠6 = 139 degrees, and ∠2 = 68 degrees. Find ∠7.
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Answer 1

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

Explanation:

l II m and p is their transversal and 1 = 120°

∠1 + ∠2 = 180 °(Straight line)

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 = ∠6 (Vertically opposite angles)

∠8 = 60°

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