Question

ABCDE is a pentagon in which angle A 95°,angleB 85°, angle C 105°,angle D 115° find angle E​

Answer 1

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A = 95°

B = 85°

C = 105°

D = 115°

E = ?

A.T.Q.

A + B + C + D + E = 540° (Sum of all angles in a pentagon)

95+85+105+115 + E = 540

E = 540-400

E = 140°

Answer 2

AnswEr :

• The measure of angle E is 140°.

⠀

Explanation :

We are given with the angle of a pentagon, that is,

• ∠A = 95°.

• ∠B = 85°.

• ∠C = 105°.

• ∠D = 115°.

We have to find out the measure of angle E.

⠀__________________________

Now,

Let us assume that, the measure of angle is "x".

As we know that

The sum of all five angles of a pentagon is 504°. This statement is known as 'angle sum property if pentagon'$.$

⇒ ∠A + ∠B + ∠C + ∠D + ∠E = 540

⇒ 95 + 85 + 105 + 115 + x = 540

⇒ 180 + 105 + 115 + x = 540

⇒ 285 + 115 + x = 540

⇒ 440 + x = 540

⇒ x = 540 - 440

⇒ x = 140

Hence, the measure of angle E is 140°.

⠀

Verification :

The sum of all five angles of a pentagon is 504°.

⇒ ∠A + ∠B + ∠C + ∠D + ∠E = 540

⇒ 95 + 85 + 105 + 115 + 150 = 540

⇒ 180 + 105 + 115 + 140 = 540

⇒ 285 + 115 + 140 = 540

⇒ 440 + 140 = 540

⇒ 540 = 540

Clearly, LHS= RHS

Here both the conditions satisfy, so our answer is correct.

Hence Verified !