The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)
Step-by-step explanation:
Let us revise some facts about the supplementary angles
- Supplementary angles are two angles the sum of their measure is 180°
- The two angles could be right angles or one of them is acute and the other is obtuse
- The two angles can not be acute angles or obtuse angles
Let us take some examples to explain the facts above
∵ One of two supplementary angles is a right angle
∵ The measure of the right angle is 90°
∵ The sum of the measures of the supplementary angles is 180°
∴ 90 + the measure of the supplement angle = 180
- Subtract 90 from both sides
∴ The measure of the supplement angle = 90°
∴ The supplement of a right angle <u><em>must be</em></u> a right angle
∵ One of two supplementary angles is 70°
∵ Its measure less than 90°
∴ This angle is an acute angle
∵ The sum of the measures of the supplementary angles is 180°
∴ 70 + the measure of the supplement angle = 180
- Subtract 70 from both sides
∴ The measure of the supplement angle = 110°
∵ Its measure greater than 90°
∴ The supplement angle is an obtuse angle
∴ The supplement of an acute angle <u><em>must be</em></u> an obtuse angle
The two supplementary angles can not be acute angles because their sum is less than 180°
The two supplementary angles can not be obtuse angles because their sum is greater than 180°
The statement <em>“The supplement of an acute angle is an obtuse angle.”</em> is always true because the sum of any two supplementary angles is 180°, so if one of them less than 90° (acute), then the other must be greater than 90° (obtuse)
Learn more:
You can learn more about the supplementary angles in brainly.com/question/11175936
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