50 Points, My friend Aadi Aluwhalia needs the answer. Please answer correctly Thankyou
Answers
Answer:
Given : ABCD is a square. P is the midpoint of AB and Q is the midpoint of BC .
PD and AQ intersect at O
To Find : the measure of ∠POQ
(a) 100
(b) 90°
(0) 75
(d) 60
Solution:
ABCD is Square
AB = BC = CD = AD
P is the midpoint of AB and Q is the midpoint of BC
AP = AB/2
BQ = BC/2
= AP = BQ
Tan∠BAQ = BQ/AB = 1/2
=> ∠BAQ = Tan⁻¹(1/2)
∠PAO = ∠BAQ = Tan⁻¹(1/2)
=> ∠DAO = 90° - ∠PAO
=> ∠DAO = 90° - Tan⁻¹(1/2)
Tan∠ADP =AP/AD = 1/2
=> ∠ADP= Tan⁻¹(1/2)
∠ADO = ∠ADP = Tan⁻¹(1/2)
∠ADP + ∠APD + 90° = 180°
=> ∠APD = 90° - Tan⁻¹(1/2)
∠APO = ∠APD
∠APO = 90° - Tan⁻¹(1/2)
Comparing ΔODA and ΔOAP
∠ADO = ∠PAO = Tan⁻¹(1/2)
∠DAO = ∠APO = 90° - Tan⁻¹(1/2)
=> ΔODA ≈ ΔOAP (AA)
=> ∠DOA = ∠POA
∠DOA + ∠POA = 180° ( linear pair)
=> ∠DOA + ∠DOA = 180°
=> 2∠DOA = 180°
=> ∠DOA = 90°
∠POQ = ∠DOA ( vertically opposite angles)
=> ∠POQ = 90°
measure of ∆POQ is: 90°
Henceforth, the correct options is (b) 90°.
Answer:
Given : ABCD is a square. P is the midpoint of AB and Q is the midpoint of BC .
PD and AQ intersect at O
To Find : the measure of ∠POQ
(a) 100
(b) 90°
(0) 75
(d) 60
Solution:
ABCD is Square
AB = BC = CD = AD
P is the midpoint of AB and Q is the midpoint of BC
AP = AB/2
BQ = BC/2
= AP = BQ
Tan∠BAQ = BQ/AB = 1/2
=> ∠BAQ = Tan⁻¹(1/2)
∠PAO = ∠BAQ = Tan⁻¹(1/2)
=> ∠DAO = 90° - ∠PAO
=> ∠DAO = 90° - Tan⁻¹(1/2)
Tan∠ADP =AP/AD = 1/2
=> ∠ADP= Tan⁻¹(1/2)
∠ADO = ∠ADP = Tan⁻¹(1/2)
∠ADP + ∠APD + 90° = 180°
=> ∠APD = 90° - Tan⁻¹(1/2)
∠APO = ∠APD
∠APO = 90° - Tan⁻¹(1/2)
Comparing ΔODA and ΔOAP
∠ADO = ∠PAO = Tan⁻¹(1/2)
∠DAO = ∠APO = 90° - Tan⁻¹(1/2)
=> ΔODA ≈ ΔOAP (AA)
=> ∠DOA = ∠POA
∠DOA + ∠POA = 180° ( linear pair)
=> ∠DOA + ∠DOA = 180°
=> 2∠DOA = 180°
=> ∠DOA = 90°
∠POQ = ∠DOA ( vertically opposite angles)
=> ∠POQ = 90°
measure of ∆POQ is: 90°
Henceforth, the correct options is (b) 90°.