Question

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

Answer 1

The measure of each interior angle of the convex pentagon is 36 degrees, 72 degrees, 108 degrees, 144 degrees, and 180 degrees.

Step-by-step explanation:

A convex pentagon has five interior angles. Let's assume that the measures of these angles are 4x, 8x, 12x, 16x, and 20x.

Since the sum of the interior angles of a pentagon is 540 degrees, we can write the equation:

4x + 8x + 12x + 16x + 20x = 540

By solving the equation, we find:

• x = 9

Therefore, the measure of each interior angle of the convex pentagon is:

• 4x = 36 degrees
• 8x = 72 degrees
• 12x = 108 degrees
• 16x = 144 degrees
• 20x = 180 degrees

Answer 2

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`°