Question

The interior angles of a pentagon are (y+13),(y+15),(y+25),(y+29),(y+40).
(A) find the value of y.
(B) find the value of each interior angles.

Answer 1

(A) The sum of the interior angles of a pentagon is 540 degrees, so we can set up an equation:

(y+13) + (y+15) + (y+25) + (y+29) + (y+40) = 540

Simplifying this equation, we get:

5y + 122 = 540

Subtracting 122 from both sides, we get:

5y = 418

Dividing by 5, we get:

y = 83.6

Therefore, y is approximately equal to 83.6.

(B) We can now use this value of y to find each interior angle:

(y+13) = (83.6+13) = 96.6 degrees
(y+15) = (83.6+15) = 98.6 degrees
(y+25) = (83.6+25) = 108.6 degrees
(y+29) = (83.6+29) = 112.6 degrees
(y+40) = (83.6+40) = 123.6 degrees

Therefore, the interior angles of the pentagon are 96.6 degrees, 98.6 degrees, 108.6 degrees, 112.6 degrees, and 123.6 degrees.