THE EXTERNAL ANGLE OF A TRIANGLE IS SUM OF OPPOSITE INTERNAL ANGLES

Hello maths bugs(🐞) and hivers(🐝)
I hope you are strong and stout and doing good in life.

Once again I have come up with another geometric property.We know that for a triangle any external angle is equal to to sum of opposite internal angles.Today using this problem I wanna solve an interesting problem as you can see in the following figure.

img_0.3364150512122516

To find value of x° our first construction is line segment DE which is equal to DC. So angle DEC and angle ECD are same value of 30° according to construction and given data.Check it in the figure below.To find sum of which two internal angles is equal to which opposite angle use color combination.
img_0.7784754614799281

The only two constructed line segments are shown below:

img_0.33394459501521895

If you use the figure given below , you find ∆BDE an equilateral triangle.Hence all of the angles of it are 60°. To find it we can use angle sum property of a triangle.

Angle BED is equal to 60° as sides of ∆BDE are equal.

img_0.37385471277566595

To reach the final segment of the solution we need to find the value of angle AEB or angle BEC. Both of them are right angle triangle.Angle BEC equal to sum of angle BED and angle DEC. That means 60°+ 30° equal to 90°.Again as angle EAD and angle EDA are equal and the value is 15° and according to the property of the tropic angle ABE equal to angle EAB and both of them is equal to 45°. And the value of x thus 45° minus 15° equals to 30°.. Bravo! Check it below:
img_0.7559453992515598

Here are some of my article which you may have like:

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I hope you enjoyed the solution to find the value of X.

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Regards: @meta007

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