Question

Four angles in a hexagon are 110° each. The remaining two angles are in the ratio 2:3. Find the smallest of these two angles.​

Answer 1

Answer:

-Two angles of hexagon are 120and 160No. of sides of hexagon = 6As we know thatSum of interier angles of any polygon = (n - 2) × 180° where n= ..

Answer 2

Given :-

• Four angles in a hexagon are 110° each.
• The remaining two angles are in the ratio 2:3.

To Find :-

• Find the smallest of these two angles.​

Solution :-

~Here, we're given that four angles in a hexagon are 110° each and the remaining two angles are in the ratio 2 : 3 . We need to find the smallest of these two angles. We'll get the measure of those four angles and we can assume other two according to their ratios given to us. Then , we'll form an equation knowing the sum of all angles in a hexagon and after solving that equation we'll get the required answer.

_____________

As we know that ,

★ Sum of all angles of a hexagon is 720°

Let the angles of the hexagon be

∠1

∠2

∠3

∠4

∠5

∠6

Measure of those four angles :

∠1  = 110°

∠2 =  110°

∠3 =  110°

∠4 =  110°

Assuming the measure of remaining angles :

∠5 = 2x

∠6 = 3x

[ According to the given ratios ]

According to the question :-

⟶ ∠1  + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 720°

⟶ 110° + 110° + 110° + 110° + 2x + 3x = 720°

⟶ 440 + 5x = 720°

⟶ 5x = 720° - 440°

⟶ 5x = 280°

⟶ x = 280°/5

⟶ x = 56°

Finding remaining angles :-

⟶ 2x = 2 × 56 = 112°

⟶ 3x = 3 × 56 = 168°

_____________

Hence,

• Smallest of these two angles is 112°

Verification :-

~We can verify our answer by putting the value of remaining two angles we got in the equation we have made before.

⟶ ∠1  + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 720°

⟶ 110° + 110° + 110° + 110° + 112° + 168° = 720°

⟶ 440° + 280° = 720°

⟶ 720° = 720°

LHS = RHS  , Hence verified !