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EXPLAIN ANSWER PLS, GIVING 100 POINTS

How many triangles can be constructed
with angles measuring 16˚, 38˚ and 126˚?
Circle one answer:
A) None
B) One
C) Infinite (More than one)

User Benubird
by
3.2k points

2 Answers

4 votes

Answer:

I'm pretty sure it would be more than one right? if i'm wrong i'm sorry

Step-by-step explanation:

User Kasiem
by
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3 votes

Answer: C) Infinite

Step-by-step explanation:

Let's see if the three angles add to 180

16+38+126 = 180

This tells us that a triangle is possible with these angles. In fact, infinitely many triangles are possible. This is because we can shrink or enlarge the triangle to whatever size we want. All that matters is that we keep the same shape but can alter the size.

Another way to think about it is to imagine walking closer to the triangle (aka enlarge it) or walk away from the triangle (to make it shrink).

As you can see, knowing the angles and nothing about the sides isn't enough information to nail down a unique triangle. This is why all of the congruence theorems of SSS, SAS, ASA, etc all involve information about at least one pair of sides.

User Kevin Meier
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3.4k points