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Q.


The larger of two supplementary angles exceeds the smaller by 18 degrees. The angles are:

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a

90 °  , 30 °  

b

30 °  , 20 °  

c

99 °  , 81 °  

d

40 °  , 30 °     

answer is C.

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Detailed Solution

Given the larger of two supplementary angles exceeds the smaller by 18 degrees.
Supplementary angles = x and y.
Let x be the larger angle and y be the smaller angle.
As we know that,
x+y= 180 °  
Also, according to the question,
x−y= 18 °  
From x+y= 180 °  ,
y= 180 ° −x  
Putting in other equation,
x−( 180 ° −x)= 18 °  
2x= 198 °  
x = 99
Now, value of y is,
x+y= 180 °  
99 ° +y= 180 °  
y= 180 ° − 99 °  
y= 81 °   The measure of 2 angles is 99 °  , 81 °  .
Hence, option 3 is correct.
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