Question

the measur if two adjacent angle of a parrallelogram are in the ratio 3:2 find the measure of each of the angles of the parrallelogram​

Answer 1

Answer:

if the ratio is 3:2, then the adjacent angles are 72 and 108. Please find the attached image for further explanation

Answer 2

$\huge\sf\pink{Answer}$

☞ Angles are 72,108,72,108

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$\huge\sf\blue{Given}$

✭ Measure of two adjacent parallelogram are of the ratio 3:2

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

◈ All this other angles?

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$\huge\sf\purple{Steps}$

$\sf \large\underline{\underline{\sf Concept}}$

In a parallelogram the opposite Angles are equal and adjacent angles add up to 180°. Here we will first find the value of the advent angles and then use the property that opposite Angles are equal

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So we know that corresponds angles in a triangle add up to 180°

➝ $\sf \angle ADC + \angle DCB = 180^{\circ}$

➝ $\sf 2x+3x=180^{\circ}$

➝ $\sf 5x = 180^{\circ}$

➝ $\sf x=\dfrac{180}{5}$

➝ $\sf \orange{x = 36}$

So the angles are,

➳ $\sf 2x = 2\times 36 = 72^{\circ}$

➳ $\sf 3x = 3\times 36 = 108^{\circ}$

As opposite Angles are equal,

»» $\sf \angle ADC = \angle ABC$

»» $\sf \angle ABC = 72^{\circ}$

Similarly,

»» $\sf \angle DCB = \angle DAB$

»» $\sf \angle DAB = 108^{\circ}$

$\sf \star\: Diagram \:\star$

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(0,0)(0,0)(1,3)\qbezier(3,0)(3,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(0,0)(0,0)\put(-0.3,-0.2){ \sf A }\put(3.1,-0.2){ \sf B }\put(4,3){ \sf C }\put(0.7,3){ \sf D }\qbezier(0.9,2.6)(1.3,2.5)(1.4,2.99)\qbezier(3.6,3)(3.8,2)(3.9,2.69)\put(1,2.3){ \sf 3x }\put(3.3,2.4){ \sf 2x }\end{picture}$

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