To determine which angle can be the measure of the second supplementary angle when one of the angles is acute (an acute angle is less than 90°), we need to know that supplementary angles add up to 180°.
Given the options:
(a) 60°
(b) 90°
(c) 120°
(d) 240°
We need to check each option to see if it qualifies based on the fact that the sum of the two angles should be 180°, and one angle must be acute.
1. Option (a): 60°
- If one of the angles is acute, it could be less than 90°. Let's denote that angle by [tex]\( x \)[/tex].
- The other angle would then be [tex]\( 180 - x \)[/tex].
- If [tex]\( x \)[/tex] is less than 90°, [tex]\( 180 - x \)[/tex] must be greater than 90°.
- If we assume the second angle is 60°, then [tex]\( 180 - x = 60 \Rightarrow x = 120 \)[/tex], which is not less than 90°. Therefore, this does not qualify.
2. Option (b): 90°
- If the other angle is 90°, then the acute angle would still be less than 90°.
- Hence, if one angle is 90°, the second angle cannot be acute, because 90° + 90° = 180°, and 90° is not an acute angle.
3. Option (c): 120°
- If one of the angles is acute and the other angle is 120°, the acute angle [tex]\( x \)[/tex] must satisfy [tex]\( x < 90 \)[/tex].
- Here, [tex]\( 180 - 120 = 60 \)[/tex] would be the measure of the acute angle, which qualifies because 60° is less than 90°.
4. Option (d): 240°
- If one of the angles is 240°, then [tex]\( 180 - 240 \)[/tex] would be negative, which is not possible for an angle measure.
Therefore, the only measure that qualifies and maintains the condition that one of the angles is acute is:
(c) 120°
