Question

b). Four angles of pentagon are 90°

, 85°

, 130°

, 100°

. Find the fifth angle​

Answer 1

Answer :

›»› The fifth angle of pentagon is 135°.

Step-by-step explanation :

Given :

• Four angles of a pentagon = 90°, 85°, 130°, 100°.

To Find :

• Fifth angle of a pentagon = ?

Knowledge required :

The sum of all five angles of a pentagon is 540°.

This statement is known as angle sum property of pentagon.

Solution :

Let us assume that, the fifth angle of a pentagon is "x".

As we know that

The sum of all five angles of a pentagon is 540°.

→ 90 + 85 + 130 + 100 + x = 540

→ 175 + 130 + 100 + x = 540

→ 305 + 100 + x = 540

→ 405 + x = 540

→ x = 540 - 405

→ x = 135.

Hence, the fifth angle of pentagon is 135°.

Verification :

The sum of all five angles of a pentagon is 540°.

→ 90 + 85 + 130 + 100 + 135 = 540

→ 175 + 130 + 100 + 135 = 540

→ 305 + 100 + 135 = 540

→ 405 + 135 = 540

→ 540 = 540.

Clearly, LHS = RHS.

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

Hence Verified !

Answer 2

Answer:

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