Question

Five angles of 7 sides regular palygon are each 136°.
If the remaining 2 angles are equal Calculate the
size of each equal angles.​

Answer 1

Size of each equal angle of a polygon is 110°

Step-by-step explanation:

GIVEN

• 5 angles = 136° each

• 2 angles are equal

TO FIND

• Size of each equal angle of a polygon

___________________________

Let's take the angles as x°

We know that,

• 5 × 136° = Measures of Five angles

• 2 × x° = Measure of 2 equal angles

• 5 × 136° + 2 × x° = Sum of all interior angles of polygon

We know that,

• Sum of all interior angles of polygon = ( n - 2 ) × 180°

• Sum of all interior angles of polygon = ( 7 - 2 ) × 180°

• Sum of all interior angles of polygon = 5 × 180°

• Sum of all interior angles of polygon = 900°

We know that,

• 5 × 136° + 2 × x° = Sum of all interior angles of polygon

• 680° + 2x = 900°

• 2x = 900° - 680°

• 2x = 220° / 2

• x = 110°

x = 110°

Size of each equal angle of a polygon is 110°

Answer 2

→ Answer :

5 angles = 136° each

2 angles are equal

TO FIND

Size of each equal angle of a polygon

___________________________

Let's take the angles as x°

We know that,

5 × 136° = Measures of Five angles

2 × x° = Measure of 2 equal angles

5 × 136° + 2 × x° = Sum of all interior angles of polygon

We know that,

Sum of all interior angles of polygon = ( n - 2 ) × 180°

Sum of all interior angles of polygon = ( 7 - 2 ) × 180°

Sum of all interior angles of polygon = 5 × 180°

Sum of all interior angles of polygon = 900°

We know that,

5 × 136° + 2 × x° = Sum of all interior angles of polygon

680° + 2x = 900°

2x = 900° - 680°

2x = 220° / 2

x = 110°

x = 110°

Size of each equal angle of a polygon is 110°

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