Question

Two opposite angles of a parallelogram are (5x-21°) and (x+75°) find the measures of the angles

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{Given}\begin{cases}\sf{Opposite\: angles\:of\: parallelogram}\\ \sf{ \implies 5x-21{}^{\circ}\:\:and\:\: x+75{}^{\circ}}\end{cases}$

• it is given that the opposite angles of parallelogram

• we know that the sum of opposite angles of parallelogram

• =>180°

Know :-

$\bf\underline{\underline{According\:to\: question:-}}$

$\sf\implies 5x-21{}^{\circ}+x+75{}^{\circ}=180{}^{\circ}\\ \\ \sf\implies 6x+54{}^{\circ}=180{}^{\circ}\\ \\ \sf\implies 6x=180{}^{\circ}-54{}^{\circ}\\ \\ \sf\implies 6x=126{}^{\circ}\\ \\ \sf\implies x=\cancel{\frac{126}{6}}\\ \\ \sf\implies x=21{}^{\circ}$

• The value of x is 21°

• Now The angels of prallelogram

$\sf\underline{\purple{\longmapsto 5x-21{}^{\circ}}}$

$\sf \implies 5\times 21{}^{\circ}-21{}^{\circ}\\ \\ \sf\implies 105{}^{\circ}-21{}^{\circ}\\ \\ \sf\implies 84{}^{\circ}$

$\sf\underline{\purple{\longmapsto x+75{}^{\circ}}}$

$\sf\implies 21{}^{\circ}+75{}^{\circ}\\ \\ \sf\implies 96{}^{\circ}$

• The two opposite angles of paralleogram is 84° and 96°

$\boxed{\boxed{\boxed{\sf{\red{VERIFICATION}}}}}$

• Let me check of their sum is 180° then it is correct

$\sf\longmapsto 84{}^{\circ}+96{}^{\circ}=180{}^{\circ}\\ \\ \sf\longmapsto 180{}^{\circ}=180{}^{\circ}$

$\sf\:\:\:\: L.H.S=R.H.S\:\:\:\:\: \mathfrak{\underline{ hence\: vertified !!}}$

$\boxed{\boxed{\mathfrak{\purple{Angles=84{}^{\circ}\:\:and\:\: 96{}^{\circ}}}}}$

#BAL

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