Question

Please tell how the answer is 112° with full explanation
I have exam on Wednesday
Class 9th
Chapter Quadrilaterals
Don't even try to post irrevalent answers or your 10 answers will be deleted​

Answer 1

★ Question:

If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is _________.

★ Solution:

Let the smallest angle of the parallelogram be x.

So the other angle will be 2x - 24.

→ We know that a property of a parallelogram is that the opposite angles of a parallelogram are equal.

So, the four angles of the quadrilateral are:

x, 2x - 24, x and 2x - 24.

According the angle sum property, the sum of all the angles is 360°.

So, forming an equation:

x + 2x - 24 + x + 2x - 24 = 360°

→ Combining the like terms:

6x - 48 = 360°

6x = 360 + 48

6x = 408

So, x = 408/6

x = 68°

So, the other angle, 2x - 24 is

(2 x 68) - 24

= 136 - 24

= 112°

Hence the measure of the largest angle of the parallelogram is 112°.

Angle Sum Property of Quadrilaterals:

The angle sum property of quadrilaterals state that the sum of all the angles of any quadrilateral will always be 360°.

→ Property of parallelogram used:

The opposite angles of any parallelogram will always be equal in measure. This means that one pair of opposite angles will have equal measure and the other pair of opposite angles will have the same measure. When all the opposite angles will have the same measure, i.e. 90°, then it becomes a rectangle.

Answer 2

★Given:-

• One angle of parallelogram is 24° less than twice the smallest angle.

★To find:-

• The measure of largest angle of parallelogram.

★Solution:-

Let,

• The smallest angle of parallelogram is x.

→Twice of the smallest angle = 2x

Given that,other angle is 24° less than twice of the smallest.

Hence,

• Other angle = 2x-24°

✦The opposite angles of a parallelogram are equal.

So,the four angles of the parallelogram are,

• x,2(x-24),x,2(x-24)

✦Sum of all angle of a quadrilateral is 360°.

And we know parallelogram is a quadrilateral.

Therefore,

➫x + 2(x-24)+x+2(x-24) = 360°

➫6x - 48° = 360°

➫6x = 360° + 48°

➫6x = 408°

➫x = 68°

Therefore,the smallest angle is 68°.

We have,

Largest angle = 2x - 24

➫ 2(68) - 24

➫ 112°

Hence,the largest angle of the parallelogram is 112°

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Know more:-

Properties of Quadrilateral:-

• A quadrilateral is a closed shape with 4 sides
• Sum of all the internal angles is 360°.

Properties of parallelogram:-

• Opposite angles are equal
• Opposite sides are equal
• Opposite sides are parallel
• Diagonals bisect each other
• Sum of any two adjacent angles is 180°

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