Question

A bathroom is shaped like a pentagon. A handyman wants to know if a corner shelf with an 80° angle will fit into the corner marked on the diagram. The sum of the angles in a pentagon is 540°. Which statement is correct?

A. The shelf angle is too big because the corner is less than 80°.
B. The shelf angle is too small because the corner is more than 80°.
C. The shelf will fit exactly because the corner is 80°.
D. It cannot be determined if the shelf will fit in that corner.

Answer 1

Okay it depends on if this is a regular pentagon or an irregular pentagon. Now if it is a regular pentagon, the answer will be B. because in a regular pentagon each angle is 108 degrees. Now if the pentagon is irregular this can not be determined which is D. because we do not know what the measurements are for the other pentagon angles. I'm sorry if this does not make complete sense, if there is a way to make this clearer, I'll be more than happy to help, just ask in the comments! Thank you! :D 

Answer 2

The correct answer is C. The shelf will fit exactly because the corner 80 degrees