Question

Find the angles of quadrilateral, if the ratio of their angles is 10:11:9:6​

Answer 1

Answer:

The angles of the quadrilateral are 100°, 110°, 90° and 60°.

Step-by-step explanation:

Given:-

Ratio of the angles of the quadrilateral = 10 : 11 : 9 : 6

To find:-

Angles of the quadrilateral

Solution:-

Let the angles of the quadrilateral be $10x$, $11x$, $9x$ and $6x$

Using the angle sum property of a quadrilateral,

$10x+11x+9x+6x=360$°

$36x=360$°

$x=\frac{360}{36}$

$x=10$°

$10x=10(10)$

$10x=100$°

$11x=11(10)$

$11x=110$°

$9x=9(10)$

$9x=90$°

$6x=6(10)$

$6x=60$°

∴ The angles of the quadrilateral are 100°, 110°, 90° and 60°.

Answer 2

$\large\sf\underline{Given\::}$

• Ratio of angles of quadrilateral = 10 : 11 : 9 : 6

‎

$\large\sf\underline{To\:find\::}$

• Measure of all the angles

‎

$\large\sf\underline{Assumption\::}$

In this question the measure of angles of a quadrilateral is given in the form of ratio. So let's assume that the common multiple be x .

Therefore :

• $\sf\:∠A\:=\:10x$

• $\sf\:∠B\:=\:11x$

• $\sf\:∠C\:=\:9x$

• $\sf\:∠D\:=\:6x$

‎

$\large\sf\underline{Property\:to\:be\:used\::}$

From the angle sum property of quadrilateral we know that :

★ $\small{\mathfrak\blue{∠A+∠B+∠C+∠D\:=\:360°}}$

‎

$\large\sf\underline{Solution\::}$

Let's use the property by substituiting the assumed value of all four angles :

$\sf\implies\:10x+11x+9x+6x=360°$

$\sf\implies\:21x+9x+6x=360°$

$\sf\implies\:30x+6x=360°$

$\sf\implies\:36x=360°$

• Transposing 36 to the other side it goes to the denominator

$\sf\implies\:x=\frac{360°}{36}$

• Reducing it to lower term

$\sf\implies\:x=\cancel{\frac{360°}{36}}$

$\small{\underline{\boxed{\mathrm\red{\implies\:x\:=\:10}}}}$ ✧

‎

Now let's substitute the value of x in the assumed value of all the four angles to get the measure of angles :

• $\sf\:∠A\:=\:10 \times 10$=$\tt\orange{100°}$ ⍟

• $\sf\:∠B\:=\:11 \times 10$ = $\tt\orange{110°}$ ⍟

• $\sf\:∠C\:=\:9 \times 10$ = $\tt\orange{90°}$ ⍟

• $\sf\:∠D\:=\:6 \times 10$ = $\tt\orange{60°}$ ⍟

_______________________

Not sure if we got the measure of angles correct !?

Let's verify it :

‎

$\sf\:∠A+∠B+∠C+∠D=360°$

• Substituiting the values we got

$\sf\leadsto\:100°+110°+90°+60°=360°$

$\sf\leadsto\:210°+90°+60°=360°$

$\sf\leadsto\:300°+60°=360°$

$\sf\leadsto\:360°=360°$

$\bf\leadsto\:LHS=RHS$

$\dag\:\underline{\sf hence\:verified\:\dag}$

‎

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!! Hope it helps !!