Q:

What are some examples of acute angles found in real life?

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A ramp forms an acute angle in relation to the ground, and a ladder forms an acute angle when leaned against a building. The sharply angled, pointed shape of a slice of pizza is another common example. One famous acute angle in pop culture occurs when the character Pac-Man opens his mouth to devour the dots.

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In geometry, an angle is the endpoint, or vertex, formed when two line segments meet. Acute angles are always positive values measuring more than 0 degrees and less than 90 degrees, giving them their sharp, or acute, shape. In contrast, an obtuse angle measures between 90 and 180 degrees, creating a wider angle and a more "blunt" vertex. When a triangle has three vertices that all form acute angles, it is known as an acute triangle. For example, an acute triangle could have an 80-degree angle, a 55-degree angle and a 45-degree angle.

All acute angles have a complement, and collectively they add up to 90 degrees. For instance, if the acute angle is 63 degrees, its complementary angle is 27 degrees. When an acute angle is accompanied by a supplementary angle, they add up to 180 degrees. The supplement of an acute angle is always an obtuse angle. In the case of a ramp, the "inner" 55-degree angle formed between the upper ramp surface and the ground directly below is acute. The "outer" 125-degree angle formed by the ramp surface, and the adjacent ground is supplementary.

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