how to solve this maths sum?
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n, AO and BO are the bisectors of angle A and angle B respectively.
∴ ∠1 = ∠4 and ∠3 = ∠5 ... (1)
To prove: ∠2 = 1/2(∠C + ∠D)
Proof:
In quadrilateral ABCD
∠A + ∠B + ∠C + ∠D = 360°
1/2(∠A + ∠B + ∠C + ∠D)=1/2(360)
1/2(∠A + ∠B + ∠C + ∠D)=180...........(2)
Now in ΔAOB
∠1 + ∠2 + ∠3 = 180° ... (3)
equating (2) and (3),
we get
∠1 + ∠2 + ∠3 =1/2∠A+1/2∠b+1/2(∠C+∠D)
∠1 + ∠2 + ∠3 = ∠1 + ∠3 + 1/2(∠C+∠D)
∠2=1/2(∠C+∠D)
Hence proved
∴ ∠1 = ∠4 and ∠3 = ∠5 ... (1)
To prove: ∠2 = 1/2(∠C + ∠D)
Proof:
In quadrilateral ABCD
∠A + ∠B + ∠C + ∠D = 360°
1/2(∠A + ∠B + ∠C + ∠D)=1/2(360)
1/2(∠A + ∠B + ∠C + ∠D)=180...........(2)
Now in ΔAOB
∠1 + ∠2 + ∠3 = 180° ... (3)
equating (2) and (3),
we get
∠1 + ∠2 + ∠3 =1/2∠A+1/2∠b+1/2(∠C+∠D)
∠1 + ∠2 + ∠3 = ∠1 + ∠3 + 1/2(∠C+∠D)
∠2=1/2(∠C+∠D)
Hence proved
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