Question

in a quadrilateral abcd ab||cd a:d=2:3 b:c=7:8 find measure of each angle
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Answer 1

GIVEN :-

• In a quadrilateral abcd , ab || cd.
• a:d = 2:3 , b:c = 7:8.

TO FIND :-

• The measure of each angle of the quadrilateral.

SOLUTION :-

Let the ratio constant be "x".

• ∠a = 2x.
• ∠b = 3x.
• ∠c = 7x.
• ∠d = 8x.

Now, As we know that the sum of all the angle of a quadrilateral is 360°.

➳ ∠a + ∠b + ∠c + ∠d = 360°

➳ 2x + 3x + 7x + 8x = 360°

➳ 20x = 360°

➳ x = 360°/20

➳ x = 18°.

Now , from the given value of x we will find the measure of each angle of the quadrilateral.

• ∠a = 2x = 36°.
• ∠b = 3x = 54°.
• ∠c = 7x = 126°.
• ∠d = 8x = 144°.

Hence the angles of quadrilateral are 36° , 54° , 126° , 144°.

Answer 2

$\huge\mathfrak\pink{Question}$

In a quadrilateral $abcd$, $ab$║$cd$, $a:d=2:3$ and $b:c=7:8$. Find measure of each angle.

$\huge\mathfrak\pink{Given}$

• $abcd$ is a quadrilateral.

• $ab$║$cd$

• $a:d=2:3$

• $b:c=7:8$

$\huge\mathfrak\pink{To\:find}$

The measure of $∠a$, $∠b$, $∠c$ and $∠d$.

$\huge\mathfrak\pink{Solution}$

Let the measure of $∠a$, $∠b$, $∠c$ and $∠d$ are $2x°,$ $7x°,$ $8x°$ and $3x°$ respectively.

We know that:

${\red{The\:sum\:of\:all\:angles\:of\:a\:quadrilateral}}\\{\red{is\:360°.}}$

$∠a+∠b+∠c+∠d=360$

➳ $2x+7x+8x+3x=360$

➳ $20x=360$

➳ $x=(\frac{360}{20})$

➳ $x=18$

$\huge\mathfrak\pink{Hence}$

Since $x=18,$

• $∠a=2x°=(2\times{18})°=36°$

• $∠b=7x°=(7\times{18})°=126°$

• $∠c=8x°=(8\times{18})°=144°$

• $∠d=3x°=(3\times{18})°=54°$

$\huge\mathfrak\pink{Therefore}$

The measure of the angles are $36°,$ $126°,$ $144°$ and $54°$ respectively.

$\huge\mathfrak\pink{Verification}$

$∠a+∠b+∠c+∠d=360$

➳ $36+126+144+54=360$

➳ $360=360$

So, L.H.S$=$ R.H.S.

Hence, verified.

$\huge\mathfrak{\pink{Done࿐}}\\{\huge\mathfrak\blue{Hope\:this\:helps\:you.}}\\{\huge\mathfrak\orange{Have\:a\:nice\:day.}}$