Question

For each set of angles, decide if there is a possible triangle that can be created whose angles have these measures in degrees: a.) 60, 60, 60 Select | b.) 90, 90, 45 Select C.) 30, 40, 50 Select | d.) 90, 45, 45 Select e.) 120, 30, 30 Select If you get stuck, consider making a line segment. Then use a protractor to measure angles with the first two angle measures.

Answer 1

`\begin{gathered} \text{ a. Yes, a triangle can be formed.} \\ \text{ b. Yes, a triangle can be formed.} \\ \text{ c. Yes, a triangle can be formed.} \\ \text{ d. No, a triangle cannot be formed.} \\ \text{ e. No, a triangle cannot be formed.} \end{gathered}`

Explanation:

To determine if three given sides form a triangle, these sides have to comply with the following formulas:

`\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \\ \text{where,} \\ a,b\text{ and c are the given sides} \end{gathered}`

Therefore,

a) Yes, it is an equilateral triangle.

b)

`\begin{gathered} 180>45 \\ 135>90 \\ 135>90 \\ \text{ These sides can create a triangle.} \end{gathered}`

c)

`\begin{gathered} 70>50 \\ 80>40 \\ 90>30 \\ \text{ These sides can create a triangle.} \end{gathered}`

d)

`\begin{gathered} 135>45 \\ 135>45 \\ 90>90\text{ }\rightarrow\text{ FALSE} \\ \text{ These sides cannot create a triangle.} \end{gathered}`

e)

`\begin{gathered} 150>30 \\ 150>30 \\ 60>120\text{ }\rightarrow\text{ FALSE} \\ \text{ These sides cannot create a triangle.} \end{gathered}`