Classifying Angles: Acute, Obtuse, Right

An acute angle is defined as an angle that measures less than 90 degrees. This distinguishes it from other types of angles, such as right angles (exactly 90 degrees), obtuse angles (greater than 90 degrees but less than 180 degrees), and straight angles (exactly 180 degrees). Acute angles are commonly found in various geometric shapes and are essential in many mathematical concepts.

A right angle is defined as an angle that measures exactly 90 degrees. It is one of the fundamental types of angles in geometry. In contrast, acute angles measure less than 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and reflex angles exceed 180 degrees. Right angles are commonly encountered in various applications, such as in construction and design, where perpendicular lines form a right angle, ensuring stability and balance.

An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. This places it between the right angle (90 degrees) and the straight angle (180 degrees). In contrast, acute angles are less than 90 degrees, and right angles are exactly 90 degrees. Therefore, the only type of angle that fits the criteria of being more than 90 degrees and less than 180 degrees is the obtuse angle.

An acute angle is defined as an angle that measures less than 90 degrees. Since 45 degrees is less than 90, it fits the criteria for being an acute angle. In contrast, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure 180 degrees. Therefore, among the given options, an angle measuring 45 degrees is classified as acute.

An obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. Since 120 degrees falls within this range, it qualifies as an obtuse angle. In contrast, acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Thus, 120 degrees is best categorized as obtuse.

A right angle is defined as an angle that measures exactly 90 degrees. It is one of the fundamental types of angles in geometry, distinguishing it from acute angles (less than 90 degrees) and obtuse angles (greater than 90 degrees but less than 180 degrees). A straight angle, on the other hand, measures 180 degrees. Thus, the unique characteristic of a right angle is its precise measurement of 90 degrees, making it a crucial concept in various mathematical and practical applications.

An acute angle is defined as an angle that measures less than 90 degrees. Since 30 degrees falls within this range, it qualifies as an acute angle. In contrast, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure 180 degrees. Therefore, 30 degrees is categorized as acute due to its measurement being less than 90 degrees.

An angle measuring 150 degrees is classified as obtuse because it is greater than 90 degrees but less than 180 degrees. Acute angles are less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, since 150 falls within the range of obtuse angles, it is accurately identified as such.

A straight angle measures exactly 180 degrees, representing a straight line. It is formed when two rays point in opposite directions, creating a linear configuration. In contrast, acute angles are less than 90 degrees, obtuse angles are between 90 and 180 degrees, and right angles measure exactly 90 degrees. Thus, the only angle that measures precisely 180 degrees is the straight angle.

An acute angle is defined as an angle that measures less than 90 degrees. Since 75 degrees falls within this range, it qualifies as an acute angle. In contrast, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure 180 degrees. Therefore, among the options provided, 75 degrees is best categorized as an acute angle.

An angle measuring 95 degrees is classified as obtuse because it is greater than 90 degrees but less than 180 degrees. Acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, since 95 degrees falls within the range of obtuse angles, it is correctly identified as such.

An acute angle is defined as an angle that measures less than 90 degrees. Since 60 degrees is less than 90, it fits this definition perfectly. In contrast, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure 180 degrees. Therefore, an angle measuring 60 degrees is classified as acute.

An obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. Since 135 degrees falls within this range, it qualifies as an obtuse angle. In contrast, acute angles are less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, 135 degrees is best categorized as obtuse.

An acute angle is defined as an angle that measures less than 90 degrees. However, when considering angles, 0 degrees is technically the smallest angle possible, and it is also classified as an acute angle since it fits the criteria of being less than 90 degrees. Thus, while 0 degrees is not typically discussed in the context of acute angles, it is the only angle that can be considered acute in this context.

A straight angle measures exactly 180 degrees, representing a straight line. In contrast, acute angles are less than 90 degrees, right angles are exactly 90 degrees, and obtuse angles are greater than 90 degrees but less than 180 degrees. Thus, among the options provided, only a straight angle corresponds to the measurement of 180 degrees, making it the correct choice.

An obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. Since 110 degrees falls within this range, it is classified as obtuse. In contrast, acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, the angle measuring 110 degrees is correctly identified as obtuse.

An acute angle is defined as an angle that measures less than 90 degrees. Since 45 degrees falls within this range, it is classified as an acute angle. In contrast, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, the 45-degree angle is best described as acute.

A right angle is defined as an angle that measures exactly 90 degrees. It is one of the fundamental types of angles in geometry, distinguishing itself from acute angles (less than 90 degrees) and obtuse angles (greater than 90 degrees but less than 180 degrees). In contrast, a straight angle measures 180 degrees. Recognizing these definitions helps in identifying the right angle as the one that specifically meets the 90-degree criterion.

An obtuse angle is defined as an angle that measures more than 90 degrees but less than 180 degrees. Since 170 degrees falls within this range, it qualifies as an obtuse angle. In contrast, acute angles measure less than 90 degrees, right angles measure exactly 90 degrees, and straight angles measure exactly 180 degrees. Therefore, 170 degrees is best categorized as obtuse.