The figure shows ∠AOC drawn with a protractor. What type of angle is it and what is its measure? A. Acute; 35° B. Obtuse; 145° C. Acute; 145° D. Obtuse; 35° 100 100 90 “10 110 Ro 120 %o 430 ” 8 88 ” 8 8 8 2 8 3 3′
The Correct Answer and Explanation is:
The correct answer is B. Obtuse; 145°.
Explanation:
A protractor is a semicircular tool marked with degrees from 0° to 180° and is commonly used for measuring angles. In the given figure, the angle ∠AOC is drawn with its vertex at point O, and its two rays extend to points A and C. The baseline ray OA aligns with the 0° mark on the protractor, while the other ray OC reaches the 145° mark.
To determine the type of angle, we analyze its measure. Angles are classified based on their degrees:
- Acute angles are less than 90°.
- Right angles measure exactly 90°.
- Obtuse angles fall between 90° and 180°.
- Straight angles measure exactly 180°.
Since the measurement of ∠AOC is 145°, it is greater than 90° but less than 180°, categorizing it as an obtuse angle.
Understanding angle measurement is fundamental in geometry because angles define the shape and structure of various figures. Correctly identifying angles is essential in applications such as architectural design, engineering, and construction. Protractors are especially useful in physics when analyzing forces or trajectories and in mathematics for calculating trigonometric values.
By aligning one side of an angle with the protractor’s baseline and noting the intersection of the second ray with the degree markings, anyone can accurately measure an angle. In this case, the intersection at 145° clearly indicates that ∠AOC is obtuse.
Mastering angle classification aids in recognizing the geometric properties of different figures, ensuring accuracy in scientific and technical disciplines.
