Question

The measures of the interior angles of a pentagon are 2x,6x,4x-6,2x-16 and 6x+2. What is the measure, in degrees, of the largest angle?

Answer 1

Answer:

170°

Step-by-step explanation:

The formulae for getting the interior sides of an angle is 180(n-2) where n is there number of sides. And pentagon has 5 sides.

180(5-2)

180(3)=540°

Additions of the must just give 540°

2x+6x+(4x-6)+(2x-16)+(6x+2)=540°

Collect like terms

2x+6x+4x+2x+6x-6-16+2=540°

20x-20=540

20x=540+20

20x=560

x=560/20

x=28°

Which of these sides gives the greatest.

2x=2(28)=56°

6x=6(28)=168°

4x-6=4(28)-6=112-6=108°

2x-16=2(28)-16=56-15=40°

6x+2=6(28)+2=168+2=170°

The greatest of them is (6x+2)°=170°