Final Answer:
21) 102°
22) 47°
23) 78°
24) 133°
25) 47°
26) 78°
27) 133°
28) 102°
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Explanation:
Let’s go step by step. We’re told that line a is parallel to line b, and we know two angles: ∠1 = 78° and ∠2 = 47°. We need to find the rest.
First, remember these simple rules:
- Vertical angles are equal (they’re opposite each other when two lines cross).
- Corresponding angles are equal when lines are parallel.
- Alternate interior angles are equal when lines are parallel.
- Angles on a straight line add up to 180°.
Let’s start with ∠3:
- ∠1 and ∠3 are on a straight line → so ∠3 = 180° - 78° = 102°.
∠4:
- ∠4 and ∠2 are vertical angles → so ∠4 = 47°.
∠5:
- ∠5 and ∠1 are vertical angles → so ∠5 = 78°.
∠6:
- ∠6 and ∠2 are on a straight line → so ∠6 = 180° - 47° = 133°.
∠7:
- ∠7 and ∠2 are vertical angles → so ∠7 = 47°.
∠8:
- ∠8 and ∠1 are vertical angles → so ∠8 = 78°.
∠9:
- ∠9 and ∠6 are corresponding angles (because a || b) → so ∠9 = 133°.
∠10:
- ∠10 and ∠3 are vertical angles → so ∠10 = 102°.
That’s it! All angles filled in using simple rules you already know.
Parent Tip: Review the logic above to help your child master the concept of parallel lines and transversals worksheet.
