Under which angle conditions could a triangle exist? Check all that apply.

Question

Under which angle conditions could a triangle exist? Check all that apply.

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Remi 1 week 2021-11-25T15:23:13+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-25T15:24:40+00:00

    Answer:

    3 acute angles

    2 acute angles, 1 right angle

    2 acute angles, 1 obtuse angle

    Step-by-step explanation:

    The sum of the three angles in a triangle is always equal to 180^{\circ}.

    Also we have:

    – An acute angle is an angle measuring less that 90 degrees

    – A right angle is an angle measuring exactly 90 degrees

    – An obtuse angle is an angle measuring more than 90 degrees

    Let’s now analyze the different statements:

    – 3 acute angles  –> this is possible, since all the three angles measure less than 90 degrees, their sum can still be 180.

    – 2 acute angles, 1 right angle  –> also possible: one angle measures 90 degrees, while the other two together have a sum of 90, so they should be both acute

    – 1 acute angle, 1 right angle, 1 obtuse angle
    –> not possible: the right angle is 90 degrees, the obtuse angle is more than 90 degrees, so their sum is already larger than 180

    – 1 acute angle, 2 obtuse angles  –> not possible: the sum of 2 obtuse angles is more than 180 degrees

    – 2 acute angles, 1 obtuse angle –> possible: the obtuse angle is more than 90 degrees, while the two acute angles are less than 90, so they can add together to form 180 degrees

    0
    2021-11-25T15:25:06+00:00

    Answer:

    3 acute angles

    2 acute angles, 1 right angle

    1 acute angle, 1 right angle, 1 obtuse angle

    1 acute angle, 2 obtuse angles  

    2 acute angles, 1 obtuse angle

    The bold ones are right on edge 2020

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