Question

The interior angle of a pentagon is y + 13° y + 15°, y +23° y+ 29 degrees and y + 40° find the value of each interior angle

Answer 1

Let the 5 interior angles of the pentagon be represented by y + 13°, y + 15°, y + 23°, y + 29°, and y + 40°.

Since the sum of the interior angles of a pentagon is 540°, we can set up the following equation:

(y + 13) + (y + 15) + (y + 23) + (y + 29) + (y + 40) = 540

Combine like terms:

5y + 120 = 540

Subtract 120 from both sides:

5y = 420

Divide by 5:

y = 84

Now that we have found the value of y, we can substitute it back into the expressions for each interior angle to find their individual values:

y + 13 = 84 + 13 = 97°
y + 15 = 84 + 15 = 99°
y + 23 = 84 + 23 = 107°
y + 29 = 84 + 29 = 113°
y + 40 = 84 + 40 = 124°

Therefore, the interior angles of the pentagon are 97°, 99°, 107°, 113°, and 124°.