Question

The interior angle measures of a convex pentagon are consecutive multiples of 4. find the measure of each interior angle.

Answer 1

Answer:

100°, 104°, 108°, 112°,116°

Step-by-step explanation:

Let the smallest angle be $4x$. Since, the interior angles are consecutive, the other angles are $4(x+1)$,$4(x+2)$,$4(x+3)$ and $4(x+4)$.

Sum of interior angles = 540°

$4x+4(x+1)+4(x+2)+4(x+3)+4(x+4)=540$°

$20x+40=540$°

$20x=(540-40)$°

$20x=500$°

$x=(500/20)$°

$x=25$

Using the value of x to calculate the angles:

$4x=4*25=100$°

$4(x+1)=4*26=104$°

$4(x+2)=4*27=108$°

$4(x+3)=4*28=112$°

$4(x+4)=4*29=116$°