Question

The sum of two interior angles of a pentagon is 252°. The remaining interior angles are equal. Find the size of the equal angles

Answer 1

Gɪᴠᴇɴ :-

• The sum of two interior angles of a pentagon is 252°.
• The remaining interior angles are equal.

Tᴏ Fɪɴᴅ :-

• Find the size of the equal angles ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

• Sum of all Interior angles of a polygon with n - sides is :- (n - 2)*180° .

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Rest All Three Equal angles of Polygon are X° Each.

So,

→ Sum of Two interior angles + Sum of 3 Equal interior angles = sum of all Angles of pentagon.

Putting values Now, we get :-

→ 252° + 3x = (5 - 2)*180°

→ 252° + 3x = 3 * 180°

→ 252° + 3x = 540°

→ 3x = 540° - 252°

→ 3x = 288°

→ x = 96° (Ans.)

Hence, The size of the equal angles is 96° Each.

Answer 2

Answer:

If there's any Polygon with n sides, there will be (n - 2) triangles inside it.

⋆ Sum of Int. ∠s = (n – 2) × 180°

Let the Remaining three equal Angles of the Pentagon be a.

☯ According to the Question :

⇢ Sum of Angles = ∠1 + ∠2 + ∠3 + ∠4 + ∠5

⇢ (n – 2) × 180° = 252° + a + a + a

⇢ (5 – 2) × 180° = 252° + 3a

⇢ 3 × 180° = 252° + 3a

⇢ 540° = 252° + 3a

⇢ 540° – 252° = 3a

⇢ 288° = 3a

• Dividing both term by 3

⇢ a = 96°

∴ Remaining equal angles are of 96°.