Question

43. Two adjacent angles of a parallelogram are in the ratio 4:5. Find their measures. I want whole calculation

Answer 1

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☞ Angles are 80°,100°

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$\huge\sf\blue{Given}$

✭ Two adjacent Angles are of the ratio 4:5

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

◈ The measure of the angles?

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

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\sf\large{A}}\put(7.7,0.9){\sf\large{B}}\put(9.5,0.7){\sf{\sg\large{Base}}}\put(11.1,0.9){\sf\large{C}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(7.7,2){\large{\sf Height}}\put(8,1){\line(1,2){1}}\put(12.1,3){\sf\large{D}}\end{picture}$

We Know that adjacent Angles add up to 180°

So let the two angles be 4x,5x

So, calculating

➝ 4x+5x = 180°

➝ 9x = 180°

➝ $\sf x = \dfrac{180}{9}$

➝ $\sf\orange{x = 20^{\circ}}$

So now that we know the Angles we can find the Angles

»» 4x = 4×20 = 80°

»» 5x = 5×20 = 100°

If you want the other Angles also they would be 80°,100°,80°,100° [Opposite Angeles are equal]

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