Answered

Which group of interior angle measurements can form a triangle? Check all that apply.

A. [tex]\(123^\circ, 35^\circ, 22^\circ\)[/tex]

B. [tex]\(55^\circ, 60^\circ, 60^\circ\)[/tex]

C. [tex]\(90^\circ, 86^\circ, 40^\circ\)[/tex]

D. [tex]\(47^\circ, 71^\circ, 62^\circ\)[/tex]

E. [tex]\(110^\circ, 30^\circ, 40^\circ\)[/tex]



Answer :

GinnyAnswer
To determine which groups of interior angle measurements can form a triangle, we need to check if the sum of the three angles in each group equals [tex]\(180^\circ\)[/tex]. A group of angles can form a triangle if and only if their sum is [tex]\(180^\circ\)[/tex].

Let's examine each group step-by-step:

1. Group: [tex]\( 123^\circ, 35^\circ, 22^\circ \)[/tex]
- Sum: [tex]\( 123^\circ + 35^\circ + 22^\circ = 180^\circ \)[/tex]
- Since the sum is [tex]\(180^\circ\)[/tex], this group can form a triangle.

2. Group: [tex]\( 55^\circ, 60^\circ, 60^\circ \)[/tex]
- Sum: [tex]\( 55^\circ + 60^\circ + 60^\circ = 175^\circ \)[/tex]
- Since the sum is not [tex]\(180^\circ\)[/tex], this group cannot form a triangle.

3. Group: [tex]\( 90^\circ, 86^\circ, 40^\circ \)[/tex]
- Sum: [tex]\( 90^\circ + 86^\circ + 40^\circ = 216^\circ \)[/tex]
- Since the sum is not [tex]\(180^\circ\)[/tex], this group cannot form a triangle.

4. Group: [tex]\( 47^\circ, 71^\circ, 62^\circ \)[/tex]
- Sum: [tex]\( 47^\circ + 71^\circ + 62^\circ = 180^\circ \)[/tex]
- Since the sum is [tex]\(180^\circ\)[/tex], this group can form a triangle.

5. Group: [tex]\( 110^\circ, 30^\circ, 40^\circ \)[/tex]
- Sum: [tex]\( 110^\circ + 30^\circ + 40^\circ = 180^\circ \)[/tex]
- Since the sum is [tex]\(180^\circ\)[/tex], this group can form a triangle.

Based on our calculations, the groups of interior angle measurements that can form a triangle are:

- [tex]\( 123^\circ, 35^\circ, 22^\circ \)[/tex]
- [tex]\( 47^\circ, 71^\circ, 62^\circ \)[/tex]
- [tex]\( 110^\circ, 30^\circ, 40^\circ \)[/tex]

These groups are the ones that satisfy the condition for forming a triangle.

Other Questions