This geometry problem looks challenging at first glance, but it can be solved easily using two fundamental angle rules.
Let’s look at the given image to gather all the necessary facts.
We have a triangle formed by intersecting straight lines on a surface.
Inside the triangle, one angle is clearly given as 60°.
Outside the triangle at the bottom-left vertex, an exterior angle is given as 140°.
At the top vertex, an exterior angle is marked as x°.
Our main goal is to calculate the exact numerical value of x.
To solve this step by step, we first need to find the interior angles of the triangle.
Observe the bottom-left vertex where two straight lines intersect.
The angle measuring 140° and the interior angle at that vertex lie on a straight line, making them supplementary angles.
Angles on a straight line always add up to 180°.
So, the interior angle at the bottom-left vertex is:
180° – 140° = 40°.
Now we know two interior angles of the triangle: 40° and 60°.
Next, we can easily find the third interior angle at the top vertex.
The sum of all interior angles in any triangle is always 180°.
Let’s add the two known interior angles together:
40° + 60° = 100°.
Now, subtract this sum from 180° to find the third interior angle:
180° – 100° = 80°.
So, the top interior angle of the triangle is 80°.
Finally, let’s find the value of x.
The angle x° and the top interior angle (80°) lie along the straight line forming the left side of the triangle.
Since they form a linear pair on a straight line, their sum must also equal 180°.
To find x, we simply subtract the top interior angle from 180°:
x = 180 – 80 = 100.
Alternatively, by the Exterior Angle Theorem, an exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
The exterior angle x° equals the sum of the two opposite interior angles (40° and 60°):
x = 40 + 60 = 100.
Both methods lead us to the exact same result.
Therefore, the final answer is x = 100.
