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Can someone please help me? Find the value of x:

Can someone please help me? Find the value of x:-example-1

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The figure given is a circle with two tangents meeting at point M and touching the circle at points L and N.

The angle made by the arc is 138 degrees

In order to get a better understanding, we can redraw the figure.

This is done below:

As we can see, the angle subtended by the arc LN, is 138 degrees.

There is a theorem that says the angle that a radius (such as OL) makes with a tangent

(such as LM) is 90 degrees.

This is illustrated further below:

This new image highlights the 90 degree angles the two tangents make with the radius of the circle.

Thus, we can consider quadrilateral MNOL, we can finally solve for x.

A theorem says that the sum of angles in a quadrilateral is 360 degrees.

Therefore, we can say:


\begin{gathered} x+90+90+138=360 \\ x+318=360 \\ \text{subtract 318 from both sides} \\ \\ x+318-318=360-318 \\ x=42^0 \end{gathered}

Therefore the final answer is: x = 42 degrees

Can someone please help me? Find the value of x:-example-1
Can someone please help me? Find the value of x:-example-2
User Ram Pratap
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