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.

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.