Question

Two adjacent angle of a parrellogram are in the ratio of 4:5 .find the measure of each of its angle

Answer 1

Given:-

• Ratio of adjacent angles of a parallelogram = 4:5

To Find:-

The measure of each angle.

Assumption:-

Let the common multiple of the ratio be x

1st angle = 4x

2nd angle = 5x

Solution:-

We know,

Sum of adjacent angles of a parallelogram is 180°.

Therefore,

$\sf{1st\:angle + 2nd \:angle = 180^\circ}$

= $\sf{4x + 5x = 180^\circ}$

= $\sf{9x = 180^\circ}$

= $\sf{x = \dfrac{180}{9}}$

= $\sf{x = 20}$

Now,

1st angle = 4x = $\sf{4\times 20 = 80^\circ}$

2nd angle = 5x = $\sf{5\times 20 = 100^\circ}$

Calculating the measure of other angles of the parallelogram.

We know measure of Opposite angles of a parallelogram is equal.

Hence,

3rd angle = $\sf{80^\circ}$ [Vertically Opposite to 1st angle]

4th angle = $\sf{100^\circ}$ [Vertically Opposite to 2nd angle]

Therefore,

Measure of all the angles of the parallelogram are:-

1st angle = 80°

2nd angle = 100°

3rd angle = 80°

4th angle = 100°

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More:-

• A parallelogram is a shape with its opposite angles equal.
• Sum of it's adjacent angle is always 180°
• Sum of all sides of parallelogram is 360°

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Answer 2

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we said that the two angles of a paralleogram are in the ratio and we have two find it's all angels.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Her, f1st we let the common multiple of the given ratio. Now, using Adjacent angles property which is that sum of adjacent angles is 180° Now, solving the eq. we will find the value of common multiple of both ratios Then using that value we will find the adjacent angles now, we know that opposite angles of Paralleogram are equal Using this property we will find all the angles of paralleogram which is our required answer.

Let's Do It ⚡

$\huge{\underline{\boxed{\sf AnSwer}}}$

_____________________________

Given:-

• Ratio of adjacent angles = 4:5

Find:-

• All the angle of the paralleogram

Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\qbezier(2,1)(2,2)(1.2,2)\qbezier(5,1)(5,2)(6.2,2) \put(3,2.8){ \bf Ratio=4:5 } \end{picture}$

Solution:-

◎ Let, ➊$\sf {\:}^{st}$ angle be ❝4x❞

◕ Let, ➋$\sf {\:}^{nd}$ angle be ❝5x❞

✎Now, we know that sum of adjacent angles is 180°

So,

$\sf \implies 4x + 5x = {180}^{ \circ}$

❈ Solving this eq.

$\sf \implies 4x + 5x = {180}^{ \circ}$

$\sf \implies 9x = {180}^{ \circ}$

$\sf \implies x = \dfrac{180}{9}$

$\sf \implies x = 20^{ \circ}$

♛ Substituting the value of x in angle ➊ and ➋

❏ ➊$\sf ^{st}$ angle = 4x = 4×20 = 80°

❏ ➋$\sf ^{nd}$ angle = 5x = 5×20 = 100°

✎ Now, we know that opp. angles of Paralleogram are equal.

• ➊$\bf {\:}^{st}$ angle = ➌$\bf {\:}^{rd}$ angle = 80°
• ➋$\bf {\:}^{nd}$ angle = ➍$\bf {\:}^{th}$ angle = 100°

$\underline{\boxed{\sf \therefore All \:angles\:of\: paralleogram\:are\:80^{\circ},80^{\circ},100^{\circ} and\:100^{\circ}}}$