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Determine whether the statement is true or false. If true, explain why. If false, give a counterexample.If two positive angles are supplementary, then one is obtuse...

Question

Determine whether the statement is true or false. If true, explain why. If false, give a counterexample.If two positive angles are supplementary, then one is obtuse and the other is acute.

Determine whether the statement is true or false. If true, explain why. If false, give a counterexample. If two positive angles are supplementary, then one is obtuse and the other is acute.



Answers

Determine whether the statement is true or false. If true, explain why. If false, give a counterexample.
If two positive angles are supplementary, then one is obtuse and the other is acute.

Okay, We have a statement if two angles former linear pair than their supplementary. And we want to write the converse of this. So what we're gonna do is we're gonna switch the order of the, uh, couldn't excuse me. The hypothesis in the conclusion. So we're gonna see if two angles are supplementary. Two angles are supplementary. Then they form a linear pair. Okay, so this is our converse of the original, um, of the original statement. So now we want to know. Is this true or false? Okay, if two angles are simple memory than they formal in your hair, the easiest way to prove this false is to come up with a counter example. Okay, so here's what I'm gonna do. I'm gonna say I've got an angle right here. What say this is angle and B C on. I'm going to say that this is a right angle. Okay, Now, over here, I have another angle. Okay? And this is angle X. Why Z and this one is also 90 degrees. Okay, Are these supplementary angle ABC Is he holding 90 degrees angle? X Y Z is equal to 90 degrees. Hey, angle. ABC plus angle X Y Z equals 180 degrees. So they are simple, Minnery. They are supplementary. But are they a linear payer? No, they're not a linear pair because they're not actually touching each other. They're not adjacent. A supplementary angles have to be adjacent or being a linear pair. Just to remind you a linear pair is when you have something like this home. Something like this. Okay, so, um, this angle and this angle for Malin, your pair and their supplementary, Okay? Because all in your pairs are supplementary, but not all supplementary angles formula to your hair.

This problem wants us to see if this statement is true or false. And if it's false, explain why. So it says if two angles are complimentary, so two angles are complimentary. Who we know that these two angles will you call 90 thes two angles also congruent. So if there could grow it in equal 90 then they have to equal the same thing, so each of them has to equal 45. So that's what the statement says. If two angles are complimentary, Ankergren thin, the measure of each angle is 45. This is true. There's no other two angles that I can add up that are the same number that's going to give me 90. So this statement is true.

We're gonna see if this statement is true or false. So it says a pair of acute angles can be supplementary. So in order to be supplement, Terry, these angles have to add up to equal 180 degrees fessing. The biggest possible angle that I could have for acute angles is like 89.99 repeating. Okay, so I have two angles that air 89.99 repeating then the highest possible degree I'm going to get is 1 79 point night night. I'm never gonna actually get Tau 1 80 specifically. So this is false to acute. Angles can never be supplementary.

We want to evaluate the truth of the true value of this statement. So it says a linear pair of angles is also a pair of supplementary angles. So linear pair of angles are two angles that when added together, they have to equal 180 degrees. That is their definition. They have to share aside, but they have to equal 100 degrees. So since that's in the definition of a linear pair, this is going to be true.


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