Question

two angles of quadrilateral are of
measure 65 degree and other two angle are equal. what os measure of this two angle.​

Answer 1

Given :

• Two angles of a quadrilateral measures 60° and other two angles are equal.

To Find :

• The measure the two angles.

Solution :

As we know that,

• $\underline{ \boxed{ \sf{Sum \: of \: all \: angles_{(Quadrilateral)} = 360^{\circ}}}}$

Assumption: Let us assume the other two angles as x.

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$\dashrightarrow \: \: \bf \: 65^{\circ} + 65^{\circ} + x + x = 360^{\circ}$

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$\dashrightarrow \: \: \bf \: 130^{\circ} + 2x = 360^{\circ}$

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$\dashrightarrow \: \: \bf \: 2x = 360^{\circ} - 130^{\circ}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \bf \: 2x = 230^{\circ}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \bf \: x = \cancel\dfrac{230^{\circ}}{2}$

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$\dashrightarrow \: \: \underline{ \boxed{ \bf{x = 115^{\circ}}}} \pink{ \bigstar}$

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$\therefore \: \underline{ \sf{The \: measure \: of \: other \: two \: angles \: = \: \bf{115^{\circ}}}}$

⠀⠀⠀⠀______________

V E R I F I C A T I O N :

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$\dashrightarrow \: \: \bf \: 65^{\circ} + 65^{\circ} + 115^{\circ} + 115^{\circ} = 360^{\circ}$ ⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \bf \: 130^{\circ} + 230^{\circ} = 360^{\circ}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\dashrightarrow \: \: \bf \: 360^{\circ} = 360^{\circ}$

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$\dashrightarrow \: \: \underline{\sf{\pmb{L.H.S = R.H.S}}}$

Hence, verified!

Answer 2

Step-by-step explanation:

$\huge\sf\blue{Given:} \:$

★ Two angles of a quadrilateral are of measure 65° and other two are equal.

$\huge\sf\blue{To \: Find:} \:$

★ Measure of two other angles

$\huge\sf\blue{Solution:} \:$

We know that,

Sum of all the angles (Quadrilateral ) = 360°

Let the missing two angles be x.

$\implies \displaystyle{ {65}^{ \circ} } + {65}^{ \circ} + x + x = {360 }^{ \circ}$

$\implies \displaystyle{ {130}^{ \circ} } + 2x = {360}^{ \circ}$

$\implies \displaystyle{2x = {360}^{ \circ \: } - {130}^{ \circ \: } }$

$\implies \displaystyle{2x = {230}^{ \circ \: } }$

$\implies \displaystyle{x = \cancel \frac{ {230}^{ \circ \: } }{2} }$

x = 115°

∴ The other two angles measure 115°.

Verification :

$\implies \displaystyle{ {65}^{ \circ} + {65}^{\circ \: } + {115}^{\circ \: } + {115}^{\circ \: } = {360}^{\circ \: } }$

$\displaystyle{ {130}^{\circ \: } + {230}^{\circ \: \: } = {360}^{\circ \: } }$

$\displaystyle{ {360}^{\circ \: } = {360}^{\circ \: } }$

$\displaystyle{L.H.S = R.H.S \: }$

Hence, Verified

$\huge\sf\blue{More \: \: Information :} \:$

✪ Sum of all the angles of a triangle is 180°.

✪ Sum of all the angles of a square is 360°.

✪ Area of a rectangle = Area of a parallelogram