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Q.

If two angles of a quadrilateral measure 85° and 75° respectively. The other two angles are equal, then the measure of each of these equal angles are ____°.


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Detailed Solution

If two angles of a quadrilateral measure 85° and 75° respectively. The other two angles are equal, then the measure of each of these equal angles are 100°.
Given, two angles of a quadrilateral measure 85° and 75° respectively and the other two angles are equal.
Let the two equal angles be ∠A,∠B  .
Assume the value of equal angles as x.
The value of given angles is ∠C= 85 ° ,∠D= 75 °  
Then,
Question Image ⇒∠A=x,∠B=x,∠C= 85 ° ,∠D= 75 °  
We know that, the sum of interior angles of a quadrilateral is equal to 360 °  .
 In quadrilateral ABCD,
⇒∠A+∠B+∠C+∠D= 360 °  
Substituting the values of angles,
⇒x+x+ 85 ° + 75 ° = 360 °   ⇒2x+ 160 ° = 360 °   ⇒2x= 360 ° − 160 °   ⇒2x= 200 °  
Dividing by 2 on both sides,
⇒ 2x 2 = 200 ° 2  
  ⇒x= 100 °  
Hence, ∴∠A= 100 ° ,∠B= 100 °  .
Therefore, the value of each of equal angles is 100 °   .
 
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