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Q.

If three angles of a quadrilateral are each equal to 75° , then determine the fourth angle and choose the option which represents the same.


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a

150 °

b

135 °

c

45 °

d

75 °  

answer is B.

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Detailed Solution

Given, three angles of a quadrilateral are each equal to 75° .
The angle sum property of a quadrilateral states that the sum of all the interior angles of a quadrilateral is always 360 .
Now, let the measure of the fourth angle be x.
Then, by the angle sum property, we have,
75 + 75 + 75 +x= 360 225 +x= 360 x= 360 225 x= 135
So, the fourth angle of the quadrilateral measures 135 .
Hence, the correct option is (2).
 
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