83.8k views
0 votes
A convex octagon has interior angles with measures (x+55), (3x+20), 4x, (4x-10), (6x-55), (3x+52), 3x, and (2x+30).

User Procleaf
by
8.0k points

1 Answer

2 votes

The value of x in the given convex octagon is approximately 37.43

To find the value of x in the given convex octagon, we can use the fact that the sum of the interior angles of an octagon is 1080 degrees.

The given interior angles are (x+55), (3x+20), 4x, (4x-10), (6x-55), (3x+52), 3x, and (2x+30).

To find x, we need to sum up these angle measures and set it equal to 1080 degrees.

(x+55) + (3x+20) + 4x + (4x-10) + (6x-55) + (3x+52) + 3x + (2x+30) = 1080

Now, let's simplify the equation by combining like terms:

28x + 32 = 1080

Next, we isolate x by subtracting 32 from both sides:

28x = 1048

Finally, we solve for x by dividing both sides by 28:

x = 1048/28

Simplifying the division, we find:

x = 37.43

Therefore, the value of x in the given convex octagon is approximately 37.43.

The complete question could be

A convex octagon has interior angles with measures (x+55), (3x+20), 4x, (4x-10), (6x-55), (3x+52), 3x, and (2x+30). Find the value of X.

User Paolo Rovelli
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories