Question

Which set of angles can be used to construct a triangle? A) 51°, 74°, and 59° B) 52°, 46°, and 82° C) 54°, 62°, and 58° D) 58°, 61°, and 57°

Answer 1

b for k12 usatestprep

Explanation:

Answer 2

B) 52°, 46°, and 82°

Explanation:

There are four sets given, we have to find out correct set of angles.

For this we have to add all the angles for each set and see which set of angles gives a total of 180°.

The angle sum property of a triangle states that sum of all the angles is equal to 180°.

A) 51°, 74°, and 59°

On adding all the angles we get;

`Sum= 51+74+59=184\°`

Here the sum is 184°, so this is not the correct set.

B) 52°, 46°, and 82°

On adding all the angles we get;

`Sum=52\°+46\°+ 82\°=180\°`

Here the sum is 180°, so this is the correct set of angles to construct a triangle.

C) 54°, 62°, and 58°

`Sum=54\°+62\°+58\°=174\°`

Here the sum is 174°, so this is not the correct set.

D) 58°, 61°, and 57°

`Sum=58\°+61\°+57\°=176\°`

Here the sum is 176°, so this is not the correct set.

Hence the correct set of angles to construct a triangle is 52°, 46°, and 82°.