Question

One angle of a pentagon is 160° find each of other angle. given that are all equal to each other

Answer 1

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

Something Before :-

• Sum of interior angles of any polygon of sides 'n' is given by a formula.

• The formula is : (n - 2) × 180°

• Pentagon has 5 sides.

• 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°

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃