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Something Before :-
- Sum of interior angles of any polygon of sides 'n' is given by a formula.
- The formula is : (n - 2) × 180°
- So, from this we can put the value of 'n' as 'n' represents the sides... in the universal formula to find sum of interior angles.
- (5 - 2) × 180° = 3 × 180° = 540°
- Therefore, the Sum of the Interior angle of a Pentagon = 540°
Required Solution :-
Let the four unknown interior angles measurement be 'x' , 'x' , 'x' & 'x' (One angle measurement is 160°)
As, Sum of interior angles of any polygon measures 560°, (Refer: Something Before)
⇒ 160° + x° + x° + x° + x° = 540°
⇒ 160° + 4x° = 540°
⇒ 4x° = 540° - 160°
⇒ 4x° = 380°
⇒ x° = 95°
∴ The measurement of each of the other angles is 95°.
Verefication :-
⇒ 160° + 95° + 95° + 95° + 95° = 540°
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