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Question
ABCD is a rectangle, if ∠BPC = 124°
Calculate:
- ∠BAP
- ∠ADP
Solution
Given:
- Rectangle ABCD
- ∠BPC = 124∘
Key Properties of a Rectangle:
- Diagonals of a rectangle bisect each other.
- Opposite angles formed by the diagonals are equal (angles around point P add up to 360∘).
Calculate ∠BAP:
-
In △ABP, diagonal AC divides ∠BAP and ∠BPC.
-
Since diagonals of a rectangle bisect each other, the total angles around point P are split symmetrically.
- Opposite angles: ∠BPC + ∠DPA = 180∘
Hence, ∠DPA = 180∘ − 124∘ = 56∘
Now, ∠BAP = `(∠DPA)/2`
`∠BAP = (56°)/2 = 28°`
Calculate ∠ADP:
Similarly, ∠ADP is the other half of ∠DPA:
`∠ADP = (∠DPA)/2 = 28°`
Final Answers:
- ∠BAP = 28∘
- ∠ADP = 28∘
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