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Q.

What does the angle in a semicircle measure?


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a

45     

b

60  

c

90  

d

36   

answer is C.

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Detailed Solution

We have to find the measure of the angle in a semi-circle.
Question ImageThe angle in a semicircle is BAC   .
From the figure,
OA=OB=OC (Radius of the same circle)
So, OA=OB
Since ∆AOB is an isosceles triangle,
ABO=OAB  
Again, OA=OC
Since ∆AOC is an isosceles triangle,
ACO=OAC  
 In ∆ABC,
ABC+BAC+ACB= 180 0 ABC+OAB+OAC+ACB= 180 0 ABC+ABO+ACO+ACB= 180 0 2×(ABO+ACO)= 180 0 [ABC=ABO,ACB=ACO] (ABO+ACO)= 180 0 2 (ABO+ACO)= 90 0  
 Observing the figure,
  BAC=OAB+OAC =ABO+ACO = 90 0   Question Image The value of the angle in a semicircle is 90  .
Therefore, option 3 is correct.
 

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