Question

The interior angles of a hexagon are in the ratio 1 : 1 : 2 : 2 : 3 : 3. Find the measure of each of its angles.

Answer 1

Answer:

Let the angles be 1x 1x 2x 2x 3x 3x

Step-by-step explanation:

1x+1x+2x+2x+3x+3x=number of sides of hexagon÷2

Answer 2

Answer:

• The angles in the hexagon are 30°, 30°, 60°, 60°, 90°,90°

Step-by-step explanation:

Given :

• The interior angles of a hexagon are in the ratio 1 : 1 : 2 : 2 : 3 : 3

To Find :

• The measure of each of its angles.

Solution :

→ Now,

• Let the angles be 1x, 1x, 2x, 2x, 3x, 3x

→ We know that,

• The sum of the interior angles in a hexagon equals 360°

→ Framing an equation,

$\longrightarrow \tt 1x + 1x + 2x + 2x + 3x + 3x = 360$

$\longrightarrow \tt 2x + 4x + 6x = 360$

$\longrightarrow \tt 12x = 360$

$\longrightarrow \tt x = \cancel\dfrac{360}{12}$

$\longrightarrow {\purple{\underline{\boxed{\pmb{\frak{x = 30}}}}\bigstar}}$

→ Now let's find the angles,

$\longrightarrow \tt 1x = 1(30) = 30$

$\longrightarrow \tt 2x = 2(30) = 60$

$\longrightarrow \tt 3x = 3(30) = 90$

→ Verification,

$\longrightarrow \tt 30 + 30 + 60 + 60 + 90 + 90 = 360$

$\longrightarrow \tt 60 + 120 + 180 = 360$

$\longrightarrow \tt 180 + 180 = 360$

$\longrightarrow \tt 360 = 360$

∴ The angles in the hexagon are 30°, 30°, 60°, 60°, 90°,90°