Question - Understanding Obtuse Angles
Solution:
An obtuse angle is one that is greater than 90 degrees but less than 180 degrees.Looking at Fig. 2.9, we see several angles, but we are only interested in those greater than 90 degrees:- The angle labeled 45 degrees is acute, not obtuse.- The angle labeled 65 degrees is acute, not obtuse.- The angle labeled 20 degrees is acute, not obtuse.- The angle labeled 30 degrees is acute, not obtuse.However, there are angles not labeled, but we can deduce their measure by looking at the image carefully:- The angle adjacent to the 65-degree angle, between the blue arrow pointing up and the blue arrow pointing to the bottom right, is obtuse because if we subtract 65 from 180 we get 115 (180 - 65 = 115), which is obtuse.- The angle adjacent to the 45-degree angle, between the blue arrow pointing up and the blue arrow pointing to the bottom left, is obtuse by the same logic: 180 - 45 = 135 degrees, which is obtuse.Therefore, from the labeled angles and considering the structure of the lines, we find two obtuse angles. The correct answer is:a) 2
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