Question

Find the measure of each interior angle given the interior angle measurement.

Answer 1

5) 72

6) 60

7) 140

8) 175

Step-by-step explanation

Let's remember the interior and exterior angle add up to 180°

so

`\begin{gathered} \text{I}_(angle)+E_(angle)\text{ =180} \\ \text{subtract I}_(angle)\text{ in both sides} \\ \text{I}_(angle)+E_(angle)-\text{I}_(angle)\text{ =180 =180}-\text{I}_(angle)\text{ =} \\ E_(angle)=\text{180}-\text{I}_(angle) \end{gathered}`

then

Step 1

5)

let

interior angle= 108

replace

`\begin{gathered} E_(angle)=\text{180}-\text{I}_(angle) \\ E_(angle)=\text{180}-108 \\ E_(angle)=72 \end{gathered}`

hence

5) 72

Step 2

6)

let

interior angle= 120

replace

`\begin{gathered} E_(angle)=\text{180}-\text{I}_(angle) \\ E_(angle)=\text{180}-120 \\ E_(angle)=60 \end{gathered}`

hence

6) 60

Step 3

7) 40

let

interior angle= 40

replace

`\begin{gathered} E_(angle)=\text{180}-\text{I}_(angle) \\ E_(angle)=\text{180}-40 \\ E_(angle)=140 \end{gathered}`

hence

7) 140

Step 4

finally,

8)5

let

interior angle= 5

replace

`\begin{gathered} E_(angle)=\text{180}-\text{I}_(angle) \\ E_(angle)=\text{180}-5 \\ E_(angle)=175 \end{gathered}`

hence

8) 175

I hope this helps you