The two angle of the quadrilateralmeasure 60 degree and 90 degree and the other two angles are equal.find the measure of the two angles.
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The two angle of the quadrilateralmeasure 60 degree and 90 degree and the other two angles are equal.find the measure of the two angles.
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Question : The two angles of the quadrilateral measure 60 degree and 90 degree and the other two angles are equal. Find the measure of the two angles.
Solution :
[tex]\bold {Given :}[/tex]
[tex]\bold {To \:Find}[/tex]
Let the measure of the two equal angles be x° .
Atq,
[tex]\boxed{\blue {Sum\: of \:all\: angles\: of\: quadrilateral = 360^{\circ}}}[/tex]
[tex]\implies 60 + 90+ x + x = 360 \\ \implies 150 + 2x = 360 \\ \implies 2x= 360-150 \\\implies 2x =210\\ \implies x= \frac{210}{2} \\ \implies x= 105 [/tex]
[tex]\boxed{\green {Hence,\:the\: measure\: of\: the\: two \:equal\: angles = 105^{\circ}}}[/tex]
[tex]\bold{Verification :}[/tex]
[tex]\implies 60^{\circ}+90^{\circ}+105^{\circ}+105^{\circ}=360^{\circ}\\ \implies 150^{\circ}+210^{\circ}=360^{\circ}\\ \implies 360^{\circ}=360^{\circ}\\ \implies LHS=RHS[/tex]
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Given ,
The two angles of quadrilateral are 60°
and 90° and the other two angles are equal
Let , the other angle be x
We know that , the sum of angles of quadrilateral is 360°
So ,
=> 60 + 90 + x + x = 360
=> 60 + 90 + 2x = 360
=> 150 + 2x = 360
=> 2x = 360 - 150
=> 2x = 210
=> x = 210/2
=> x = 105
Hence , the other two angles are 105° and 105°
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