Question

The angles of a Pentagon are (3x+5)• ,(x+16)•,(2x+9)•,(3x-8)• and (4x-15)• respectively. Find the value of x and hence find the measures of all the angles of the Pentagon​

Answer 1

Answer:

answer

Step-by-step explanation:

let the common multiple be x

let all angles be x

x+x+x+x+x= 540

5x=540

x=540÷5

x=108

angles are

3x+5=329

x+16=124

3x-8=316

4x-15=417

Answer 2

The sum of all interior angles of a polygon =(n-2)×180⁰

Where, 'n' is the number of sides of the given polygon.

The sum of interior angles of a pentagon=(5-2)×180⁰

The sum of interior angles of a pentagon=3×180⁰

The sum of interior angles of a pentagon=540⁰

According to the question,

3x+5+x+16+2x+9+3x-8+4x-15=540⁰

13x+7=540⁰

13x=540-7

13x=533

x=41⁰

As x=41⁰

3x+5=3+41⁰+5=123⁰+5⁰=128⁰

x+16=41⁰+16⁰=57⁰

2x+9=2×41⁰+9⁰=82⁰+9⁰=91⁰

3x-8=3×41⁰-8⁰=123⁰-8⁰=115⁰

4x-15=4×41⁰-15⁰=164⁰-15⁰=149⁰

Therefore,

The angles of the pentagon are 128⁰,57⁰,91⁰,115⁰,149⁰.

The value of 'x' is 41⁰.