Three of the angles of a hexagon are each Xo. The others are each 3Xo. Find X

Three of the angles of a hexagon are each X^o. The others are each 3X^o. Find X

Answer Details

The sum of the interior angles of a hexagon is given by the formula (n-2)×180^o, where n is the number of sides/angles in the polygon. Since a hexagon has six sides/angles, the sum of its interior angles is (6-2)×180^o = 4×180^o = 720^o. Let's assume that three angles of the hexagon are each X^o. Therefore, the sum of these three angles is 3X^o. The other three angles are each 3X^o, so their sum is 9X^o. Thus, the total sum of the six angles is: 3X^o + 9X^o = 12X^o But we also know that the sum of the interior angles of a hexagon is 720^o. Therefore, we can equate the two expressions: 12X^o = 720^o Dividing both sides by 12, we get: X^o = 60^o Therefore, the answer is X = 60^o.