1.

The interior angles of a quadrilateral are (2x+15), (2x - 5),(3x + 75) and (3x - 25) the smallest interior angle of the quadrilateral.

Answer»

Answer:

55°

Step-by-step explanation:

LET there is a quadrilateral ABCD.

Given that,

  • A = (2x+15)
  • B = (2x-5)
  • C = (3x+75)
  • D = (3x-25)

Now, we know that,

Sum of all INTERIOR angles of a quadrilatral is equal to 360°.

Therefore, we will get,

=> 2x+15+2x-5+3x+75+3x-25 = 360

=> (2x+2x+3x+3x) + (15-5+75-25) = 360

=> 10x + 60 = 360

=> 10x = 360-60

=> 10x = 300

=> x = 300/10

=> x = 30

Therefore, we will get,

=> A = 2(30) + 15 = 60+15

=> A = 75°

=> B = 2(30) - 5 = 60-5

=> B = 55°

=> C =3(30) + 75 = 90+75

=> C = 165°

=> D = 3(30) - 25 = 90-25

=> D = 65°

Hence, smallest of the interior angles is B, i.e., 55°, i.e., (2x-5).


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