Question

An angle of a quadrilateral measures five-third of a right angle and other three angles are equal.Find the measure of each of the equal angles.​

Answer 1

An angle of a quadrilateral measures five-third of a right angle and other three angles are equal.Find the measure of each of the equal angles.​

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Expert Answer:

Let x be one the three equal angles.

Sum of all the angles of a quadrilateral = 360o

⇒ x + x + x + 120o = 360o

⇒ 3x = 360o -120o

⇒ 3x = 240o

⇒ x = 80o

Thus, the measure of each of the equal angle is 80o

Answer 2

$\bf{\dag}\:{\underline{\sf{Question\::}}}$

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An angle of a quadrilateral measures five-third of a right angle and other three angles are equal. Find the measure of each of the equal angles.

$\bf{\dag}\:{\underline{\underline{\sf{Answer\::}}}}$

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Each of the equal angles of quadrilateral measures 70°.

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$\bf{\dag}\:{\underline{\underline{\sf{Given\::}}}}$

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One angle of quadrilateral = 5/3(Right angle)

Other three angles of quadrilateral are equal

$\bf{\dag}\:{\underline{\underline{\sf{To\:Find\::}}}}$

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Measure of each equal angles?

$\bf{\dag}\:{\underline{\underline{\sf{Solution\::}}}}$

☯ We know that, one angle of quadrilateral is 5/3 of right angle it means one angle of quadrilateral is 5/3 of 90°. Therefore;

$\begin{gathered}\\ :\implies\:\tt One\:angle = \dfrac{5}{3}\:of\:90\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt One\:angle = \dfrac{5}{\cancel{3}}\:\times\:\cancel{90}\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt One\:angle = 5\:\times\:30\end{gathered}$

$\begin{gathered}\\ :\implies\:{\underline{\boxed{\tt{One\:angle = 150^{\circ}}}}}\end{gathered}$

☯ Hence, one angle of quadrilateral measures 150° and we know that other three angles are equal.

Let each equal angle be y

We know that,

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$\quad\bigstar\:{\boxed{\sf{\pink{Sum_{(angles\:of\:quadrilateral)} = 360^{\circ}}}}}$

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Therefore,

$\begin{gathered}\\ :\implies\:\tt 150 + y + y + y = 360\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt 150 + 3y = 360\end{gathered}$

:⟹150+3y=360

$\begin{gathered}\\ :\implies\:\tt 3y + 150 = 360\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt 3y = 360 - 150\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt 3y = 360 - 150\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt 3y = 210\end{gathered}$

$\begin{gathered}\\ :\implies\:\tt y = {\cancel{\dfrac{210}{3}}}\end{gathered}$

$\begin{gathered}\\ :\implies\:{\underline{\boxed{\tt{y = 70^{\circ}}}}}\end{gathered}$

Hence, each of the equal angles of quadrilateral measures 70°.

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