Question

2 adjacent angles of a parallelogram are in ratio 3:4 find all angles of parallelogram
pls help anyone​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf Ratio \: of \: adjacent \: angles \: of \: a \: parallelogram = 3 : 4$

$\bf \underline{\underline{\maltese\: To \: find }}$

$\sf Measure \: of \: each \: angles \: of \: the \: parallelogram.$

$\bf \underline{\underline{\maltese\: Solution }}$

Let us assume that, the measures of two adjacent angles of a parallelogram be (3x) and (4x).

$\bf \underline{\underline{\maltese\: Diagram }}$

$\setlength{\unitlength}{1cm}\thicklines \begin{picture}(10,10) \qbezier(0,0)(2.5,0)(5,0) \qbezier(0,0)(0.5,1.5)(1,3) \qbezier(5,0)(5.5,1.5)(6,3) \qbezier(1,3)(3,3)(6,3) \qbezier(0.6,0)(0.6,0.3)(0.2,0.6) \qbezier(0.8,2.4)(1.4,2.4)(1.6,3) \put(1.5,2.2){\huge{\textsf{3x}}} \put(0.3,0.3){ \huge{ \textsf{4x}}} \put( - 0.5, - 0.5){ \huge{B}}\put(5, - 0.5){ \huge{C}}\put(0.5, 3.3){ \huge{A}}\put( 6, 3.3){ \huge{D}}\end{picture}$

$\bf \underline{As \: we \: know \: that} :$

$\boxed{ \purple{\sf Sum \: of \: two \: adjacent \: angles \: of \: a \: parallelogram \: is \: 180^{\circ}}}$

$\bf \underline{ Now},$

$\sf \implies 3x + 4x = 180^{\circ}$

$\sf \implies 7x = 180^{\circ}$

$\sf \implies x = \dfrac{180}{7}$

$\bf \bigstar Value \: of \: 3x$

$\sf \implies 3x = 3 \times\dfrac{180}{7}$

$\sf \implies 3x \approx 77.14285714$

$\bf \bigstar Value \: of \: 4x$

$\sf \implies 4x = 4 \times\dfrac{180}{7}$

$\sf \implies 4x \approx 102.85714285$

$\bf \underline{ Now},$

We know that, the opposite angles of a parallelogram are equal.

$\sf \angle ABC = \angle ADC$

$\sf So, \angle ADC = 102.85714285$

$\bf And$

$\sf \angle BAD = \angle DCB$

$\sf So, \angle DCB = 77.14285714$

$\bf \underline{Hence, the\: angles \:are} :$

$\sf \implies ABC =102.85714285$

$\sf \implies BAD = 77.14285714$

$\sf \implies ADC = 102.85714285$

$\sf \implies DCB = 77.14285714$