Question

May I please get help with this math problem please. I have tried several times but still is confusing

Answer 1

a) can be angle measures

b) cannot be angle measures

c) can be angle measures

d) cannot be angle measures

Step-by-step explanation:

The sum of angles in a triangle is 180 degrees. For three angles to make a triangle, their sum should be equal to 180 degrees.

`\begin{gathered} a)\text{ }85\degree,75\degree,\text{ 20}\degree \\ \text{Their sum = 85 + 75 + 20} \\ \text{Their sum = 180}\degree\text{ (This can form a tiangle)} \\ It\text{ can be angle measures of a triangle} \end{gathered}`
`\begin{gathered} b)\text{ }56\degree,\text{ 34}\degree\text{ 42}\degree \\ \text{Their sum = 56 + 34 + 42} \\ \text{Their sum = 132}\degree \\ 132\degree\text{ is less than 180}\degree\text{ } \\ \text{Hence, it cannot be angle measures of a triangle} \end{gathered}`
`\begin{gathered} c)\text{ }112\degree,\text{ 50}\degree,\text{ 18}\degree \\ \text{Their sum = 112 + 50 + 1}8 \\ \text{Their sum = }180\degree \\ \text{Hence, it can be angle measures of a triangle} \end{gathered}`
`\begin{gathered} d)\text{ }24\degree,\text{ 15}\degree,\text{ 51}\degree \\ \text{Their sum = 24 + 15 + 51} \\ \text{Their sum = 90}\degree \\ 90\degree\text{is less than 180}\degree \\ \text{Hence, it cannot be angle measures of a triangle} \end{gathered}`