Identify which type of triangle appears in the drawing:
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Identify which type of triangle appears in the drawing:
Note that the sum of angles in a triangle equals 180 degrees.
Let's calculate alpha in the following way:
Let's divide both sides by 1.5:
Now we can calculate the remaining angle in the triangle:
So in the triangle we have 3 angles: 60, 80, 40
All of them are less than 90 degrees, therefore all angles are acute angles and the triangle is an acute triangle.
Acute triangle
Find the measure of the angle \( \alpha \)
The notation means one angle is half the size of another angle. In this triangle, one angle equals α and another equals α divided by 2.
A single angle doesn't determine triangle type! You need all three angles. Even though 60° is acute, the other angles could be obtuse (>90°) or right (=90°).
Acute: All angles < 90°
Right: One angle = 90°
Obtuse: One angle > 90°
Remember: only one classification applies to each triangle!
First subtract 60 from both sides:
Then divide by 1.5 (or multiply by ):
No! If two angles were each greater than 90°, their sum would exceed 180° - but that's already the total for all three angles combined. Only one obtuse angle is possible per triangle.
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