If two angles are supplementary and one of them is an acute angle, what must the other angle be?
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Step by Step Explanation:
- The two angles are said to be supplementary if the sum of their measures is 180°.
- In the given problem, one of the angles is an acute angle which means that the angle is greater than 0° but less than 90°. It means that the other angle must be greater than 90° but less than 180°. In other words, the other angle must be an obtuse angle.
- Let us review this using the following illustration:
- In the figure above, POM is a straight angle. That is, ∠POM = 180°. The ∠MON is an acute angle and ∠PON is an obtuse angle.
- Hence, if two angles are supplementary, and one of them is an acute angle. Then the other angle must be an obtuse angle.