Question

ABCDE IS A POLYGON FIND THE SUM OF THE FIVE INTERIOR ANGLES​

Answer 1

Answer:

Step-by-step explanation:

Using the Formula 180(n - 2) for the sum of angles where "n" is the Number Of  sides.

SO,

ABCDE is 5 vertices , meaning it has 5 sides , so the sum of all angles is :

= 180 ( n - 2 )

= 180 ( 5 - 2)

= 180 ( 3 )

= 540 degree

Answer 2

Step-by-step explanation:

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♡ ↪☛ The interior angles of triangle ADC are: 36, 72, and 72 degrees.

Since this regular polygon has 5 vertices (implied from the ABCDE), it’s a regular pentagon. (This means an equilateral, equiangular pentagon.) All sides of the same length, and all interior angles of the same measure: Each interior angle = 108 deg., since it must be supplementary with each exterior angle which = 72 deg. (The sum of all ext. angles must always = 360 deg. in any convex polygon. So, 360 deg./5 =72 deg., and 180 - 72 = 108).

Segment AC forms an isosceles triangle (ABC) whose vertex angle = 108 deg. and whose base angles each = 36 deg., since its int. angles must add up to 180 deg. (108 + 36 + 36 = 180 deg.) Since base angle ACB (36 deg.) is adjacent to angle ACD of the triangle in question, the sum of the 2 angles = 108 deg. because together they form int. angle BCD of pentagon. This means angle ACD =72 deg. : 108 - 36 = 72). Angle ADC also = 72 deg. since both angles are the base angles of triangle ACD, which is also isosceles : segment AD is equal in length to AC because it forms a congruent iso. triangle with sides EA and DE of pentagon, just like segment AC forms with sides AB and BC. That leaves angle DAC, which =36 deg. because the sum of the 3 int. angles (72, 72, and 36) must = 180 as well.

♡

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