Question

the anglea of a quadralateral are in the ratip 4:3:2:6 find the measure of each angle​

Answer 1

Answer:

Step-by-step explanation:

Sum of the angles of a quadrilateral is 360°.

So, 4x + 3x + 2x + 6x = 360°

So 15x = 360°

x = 360°/15 = 25

Now just multiply the ratios with 24

4 x 24 = 96

3 x 24 = 72

2 x 24 = 48

6 x 24 = 144

Hope this helps !

Mark as brainliest !!

Answer 2

Given:

• the angles of a quadralateral are in the ratio 4:3:2:6

To Find:

• find the measure of each angle in the quadrilateral respectively!

Solution:

$\circ$ Here, we have given that the sides of a quadrilateral are in the following ratio which is 4 : 3 : 2 : 6

⇢ Now, let's assume the angles of the quadrilateral as 4x,3x ,2x ,6x

$\circ$ Now let's use suitable properties of a quadrilateral to find the measurements of the angles in the given ratio accordingly.

We know that,

• Angle sum property of a quadrilateral states that, the sum of the measurements of all the interior angles in the quadrilateral equals 360°

Applying the concept,

• Let's frame an equation which is appropriate to the condition.

Equation :

$\longrightarrow \tt \: 4x + 3x + 2x + 6x = 360 \degree$

• Now let's solve the equation...

$\longrightarrow \tt \: 4x + 3x + 2x + 6x = 360 \\ \\ \\ \longrightarrow \tt7x + 8x = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 15x = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: x = \cancel\frac{360}{15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow { \pink{ \boxed{\tt { x = 24 \degree}} {\pink{ \star}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth, the value of x is 24°

$\circ$ Now, let's find the angles respectively...

${ \purple{ \mapsto{ \tt{4x = 4(24) = 96 \degree}}}} \: \: \\ \\ { \purple{ \mapsto{ \tt{3x = 3(24) = 72 \degree}}}} \: \: \\ \\ { \purple{ \mapsto{ \tt{2x = 2(24) = 48 \degree}}}} \: \: \\ \\ { \purple{ \mapsto{ \tt{6x = 6(24) = 144 \degree}}}}$

Verification:

Let's put the values of the angles which we found in the equation and check weather their sum is 360°

$\longrightarrow \tt \: 96 + 72 + 48 + 144 = 360 \\ \\ \\ \longrightarrow \tt168 + 48 + 144 = 360 \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt 216 + 144 = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: 360 = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Hence verified!!!

Therefore:

• The angles are 96°, 72°,48°, 144° respectively

━━━━━━━━━━━━━━━━━━━━━━━━━━━

More Info:

${ \pink{ \boxed{ \tt{Exterior \: angle \: property}}}}$

• If the sides of a quadrilateral are in an order forming exterior angles then the sum of them equal 360°

${ \pink{ \boxed{ \tt{Adjecent \: sides \: and \: angles}}}}$

• Two sides of a quadrilateral are said to be adjacent sides of a quadrilateral if they havea common end

• Two angles are said to be adjacent angles it they have a common side.

${ \pink{ \boxed{ \tt{Opposite \: sides \: and \: angles}}}}$

• Two angles in a quadrilateral are set to be opposite angles if they are not adjacent

• Two sides in a quadrilateral are set to be opposite angles if they are not adjacent