Question

In a quadrilateral measure of two adjacent angles are 52° and 110° find the remaining two equal angles?

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Answer 1

$\huge{ \underline{ \overline{ \mid{ \cal{ \purple{AnSwEr \: }}}}}}{ \mid}$

$\large{ \underline{ \rm{ Given :-}}}$

Measure of 2 adjacent angles = 52° and 110°

$\large{ \underline{ \rm{ To \: find :-}}}$

Let the Remaining equal angles be x

$\small{ \boxed{ \rm{ total \: measure \: of \: quadrilateral \: = {360}^{o} }}}$

$\large{ \underline{ \rm{ Now :-}}}$

$\small{ \rm{ = > x + x + 54 + 110 = {360}^{o}}}$

$\small{ \rm{ = > 2x + 162 = {360}^{o}}}$

$\small{ \rm{ = > 2x = 360 - 162}}$

$\small{ \rm{ = > 2x = 198}}$

$\small{ \rm{ = > x = \frac{198}{2}}}$

$\small{ \rm{ = > x = 99}}$

Therefore the two equal angles are 99.

Answer 2

Given that,

• In a quadrilateral measure of two adjacent angles are 52° and 110°.

And,

• We've to find out the remaining two equal angles.

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⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━

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☯ Let's consider that the other angles of the quadrilateral be x.

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Now,

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$\dag\;{\underline{\frak{As \ we \ know \ that,}}}$

• Sum of all angles of the Quadrilateral is 360°.

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Therefore,

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$:\implies\sf x + x + 110^{\circ} + 52^{\circ} = 360^{\circ} \\\\\\:\implies\sf 2x + 162^{\circ} = 360^{\circ} \\\\\\:\implies\sf 2x = 360^{\circ} - 162^{\circ} \\\\\\:\implies\sf 2x = 198^{\circ} \\\\\\:\implies\sf x = \cancel\dfrac{198}{2} \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 99^{\circ}}}}}}$

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$\therefore\:{\underline{\sf{Remaining \ two \ equal \ angles \ measure \ is \: \bf{99^{\circ}}.}}}$