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Q.

If three angles of a quadrilateral are 76°, 54° and 108°, then the measure of the fourth angle is ____°.


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Detailed Solution

If three angles of a quadrilateral are 76°, 54° and 108°, then the measure of the fourth angle is 122°.
Given, three angles of a quadrilateral are 76°, 54° and 108°
Draw a quadrilateral ABCD,
Question ImageHere, B= 108 ° ,C= 54 ° ,D= 76 °  Assume that, A=x  
We know that, sum of all interior angles of a quadrilateral is equal to 360 °  .
In quadrilateral ABCD,
A+B+C+D= 360 °  
Substituting the values of angles,
x+ 108 ° + 54 ° + 76 ° = 360 °   .....… (2)
x+ 238 ° = 360 °  
x= 360 ° 238 °  
x= 122 °   A= 122 °  
Therefore, the value of fourth angle of quadrilateral is 122 °  .
 
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