Question

In each of the following figure , O is the centre of the circle . Find the size of each lettered angle :
Figures are given below ​

Answer 1

Answer:

(i) In the figure, AB is the diameter

and O is the centre of the circle ∠ CAB = 32°,

∠ ABD = 50° , ∠C = 90° (Angle in the semicircle)

By ∠ sum property of ∆

In ∆ABC, ∠C + ∠CAB + ∠ABC = 180°

⇒ 90° + ∠CAB + x = 180°

⇒ 32° + x = 180° – 90°

⇒ x = 90° – 32°

⇒ x = 58°

Similarly in right ∆ ADB

∠ADB = 90°

By ∠ sum property of ∆

∠ABD + ∠D + ∠BAD = 180°

⇒ 50° + 90° + ∠BAD = 180°

⇒ ∠y + 140° = 180°

⇒ ∠y = 180° – 140° = 40°

⇒ ∠y = 40°

ii) In the figure,

AC is the diameter of circle with centre O

∠DAC=37

 AD || BC

∠ACB=∠DAC (Alternate angles)

Hence,

x=37  

In Δ ABC,

∠B=90    (angle in semicircle)

By angle sum property of triangle, we get,

∠x+∠y+∠B=180  

37 +∠y+90   =180  

 ∠y=180−127

 We get,

∠y=53  

hope it helps u!!!

Answer 2

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