Question

If one angle of a Pentagon is 100° and the remaining four angles are equal,what is the measure of each equal angle?​

Answer 1

Answer:

Step-by-step explanation:

As we all know pentagon has 5 sides

x = side

100 + x + x + x+ x = 360

100 + 4x = 360

4x = 360 - 100

4x = 260

x = 260÷ 4

x = 65

∴ The measure of each equal angle are 65

Answer 2

Question :

Given one angle of pentagon is  100° and to find the other 4 angles.

Solution :

Number of angles in pentagon is 5

• One angle of pentagon is  100°

• Let the other 4 angles be x + x + x + x

Their sum = $4x + 100^\circ$

But sum of all the interior angles of a pentagon = $(2n - 4) \times 90^\circ$

$=(2 \times 5 - 4) \times 90^\circ = 540^\circ\\\\\\=3\times180=540^\circ\\\\\\\to 4x+100=540^\circ\\\\\\\to 4x=540^\circ-100^\circ\\\\\\\to 4x=440^\circ\\\\\\\to x =(\frac{440}{4})^\circ\\\\\\\to x =110^\circ$

Answer :

The measure of the equal angles is 110°

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