Question

Suppose the measures of the interior angles of convex quadrilateral are four consecutive odd numbers. find the measure of the largest angle.

Answer 1

To solve this problem you must apply the proccedure shown below:
1. By definition, you can calculate an oodd number by using the following expression:

`2n+1`
2. The problem says the measures of the interior angles of convex quadrilateral are four consecutive odd numbers. By definition, the sum of the interior angles of a convex quadrilateral is
`360 degrees`.
3. Therefore, you have:

`(2n+1)+(2n+3)+(2n+5)+(2n+7)=360`
4. Now, solve for n:

`8n+16=360 \\ n=43`
5. The measure of the largest angle is:

`=2n+7 \\ =2(43)+7 \\ =93 degrees`
The answer is:
`93 degrees`