By using the fact that the internal angles of a triangle always add up to 180°, we will see that x = 100°.
How to find the angle x?
Remember that the sum of all the internal angles of a triangle is always equal to 180°.
On the image we can see two triangles, let's define the angle at the right as A. and the angle at the left as B
We can write:
A + B + x = 180°
And for the inner triangle the angles give:
A/2 + B/2 + 140° = 180°
So we have a little system of equations:
A + B + x = 180°
A/2 + B/2 + 140° = 180°
If we multiply the second equation by 2 we get:
A + B + 280° = 360°
With the first equation we can write:
A + B = 180° - x
And replace that in the above equation
(A + B) + 280° = 360°
180° - x + 280° = 360°
Now we can solve this to get the value of x:
180° + 280° - 360° = x = 100°
We conclude that the measure of angle x is 100°
If you want to learn more about triangles:
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