What are the values of x in the equation x(x-6)=4(x+6)

1 answer:

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<span>x(x-6) = x^2 - 6x 4(x+6) = 4x + 24 First we need to eliminate the bracket by multiplying the numbers and variables from outside the bracket with the inside, we weill get : X^2 - 6x = 4x + 24 (subtract 4x and 24 from both sides) x^2 - 10x - 24 = 0 (x+2) (x-12) = 0 x+2 = 0 x-12 = 0 The value of X would be : x = -2 x = 12 </span>

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The required solution is ∠RQT = 202° and ∠QTS = 51°

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<h3>What is a cyclic quadrilateral?</h3>

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also called as inscribed quadrilateral.

Its main property is that the sum of opposite angles of inscribed quadrilateral is always 180 degrees.

Now, the given circle has a cyclic quadrilateral QRST in which it is given that ∠RQT = 202° and ∠QRS = 129°

Since,sum of the opposite angles of a cyclic quadrilateral = 180°

⇒∠QTS + ∠QRS = 180°

⇒ ∠QTS + ∠129° = 180°

⇒ ∠QTS = 180° - ∠129°

⇒ ∠QTS = 51°

Hence,the requires angles are ∠RQT = 202° and ∠QTS = 51°.

More about cyclic quadrilateral :

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