Question

A living room is shaped like a pentagon. A carpenter wants to put a triangular shelf in the corner marked on the diagram. The sum of the interior angles of a pentagon is 540°. Which statement is correct?
a.) The shelf angle is too small because the corner is more than 70°.
b.) The shelf angle is too big because the corner is less than 70°.
c.) The shelf will fit exactly because the corner is 70°.
d.) It cannot be determined if the shelf will fit in the corner.

Answer 1

Answer:

D) It cannot be determined if the shelf will fit in the corner.        

Step-by-step explanation:

We are given the following information in the question:

A living room is shaped like a pentagon.

The sum of the interior angles of a pentagon is 540°.

Given in the image the four angles in degrees of pentagon are 150, 150, 90 and 90.

The fifth angle of pentagon can be calculated as:

$540-(150+150+90+90) = 60$

Thus, the fifth angle of the pentagon is 60 degrees.

A carpenter wants to put a triangular shelf in the corner marked on the diagram.

Since we do not know anything about triangular shelf, whether it is equilateral triangle, right angled triangle, thus we cannot  determine if the shelf will fit in the corner.

d) It cannot be determined if the shelf will fit in the corner.

Answer 2

The corner is 60°, and based on the information given it is D...but if you can measure the angle, it would be B... A and C assume different sizes.