According to the data in the diagram, calculate a size of angle ABC.
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According to the data in the diagram, calculate a size of angle ABC.
Note that from the diagram we are able to determine the value of angle BAC, since its corresponding angle is equal to 105.
Now in the triangle we are given two angles:
Since the sum of angles in a triangle is equal to 180, we can calculate angle ABC:
30
Indicates which angle is greater
An interior angle is inside the triangle between two sides. An exterior angle is outside the triangle, formed when you extend one side. Look at the diagram carefully to see where the angle is positioned!
Check if some angles might be exterior angles! Remember: exterior angle = 180° - interior angle. Convert all angles to interior angles first, then apply the triangle angle sum rule.
This is a fundamental property of triangles in flat (Euclidean) geometry. No matter what shape or size triangle you have, the three interior angles will always add up to exactly 180°.
The triangle angle sum rule is essential for this type of problem. It's one of the most important geometric facts you'll use! Once you know two angles, you can always find the third.
A negative result means you made an error! Check that you're using interior angles correctly. Interior angles in triangles are always between 0° and 180°, so negative values indicate a mistake.
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