Answer:
128°
Step-by-step explanation:
Pentagon: has 5 sides
Let n be the number of sides of the polygon (pentagon).
a + (a+10) + (a+20) + (a+30) + (a+40) = (n-2) × 180
a + a + 10 + a + 20 + a + 30 + a + 40 = 3 × 180
5a + 100 = 540
5a = 540 - 100
= 440
a = 440 ÷ 5
= 88
Largest angle of the pentagon = (a+40)°
= 88° + 40°
= 128°
Answer:
largest angle = 128°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
A pentagon has 5 sides so n = 5 , then
sum = 180° × 3 = 540°
Sum the interior angles and equate to 540
a + a + 10 + a + 20 + a + 30 + a + 40 = 540 , that is
5a + 100 = 540 ( subtract 100 from both sides )
5a = 440 ( divide both sides by 5 )
a = 88
Then
largest angle = a + 40 = 88 + 40 = 128°
