Question

Hello help me with this question thanks in advance​

Answer 1

`\bold{\huge{\purple{\underline{ Solutions}}}}`

Answer 5 :-

We have,

`\sf{ HE = 2x cm \: and \: OR = ( x + 5)cm}`

We know that,

• Parallelogram has opposite sides parallel and equal.

From above property,

`\sf{ HE = OR }`

`\sf{ 2x = x + 5}`

`\sf{ 2x - x = 5}`

`\sf{ x = 5}`

Thus, The value of x is 5cm

Therefore,

The value of HE

`\sf{ = 2x}`

`\sf{ = 2× 5}`

`\sf{\red{ = 10 cm}}`

The measurement of HE is 10 cm

Hence, Option A is correct

Answer 6 :-

We have,

`\sf{m}{\sf{\angle{HER = 5y - 26° \: and\: m }}}{\sf{\angle{ ROH = 2y + 40°}}}`

• In parallelograms, Opposite angles are equal

From above property,

`\sf{m}{\sf{\angle{HER = }}}{\sf{\angle{ ROH}}}`

`\sf{ 5y - 26° = 2y + 40°}`

`\sf{ 5y - 2y = 40 + 26}`

`\sf{ 3y = 40 + 26}`

`\sf{ y = 66/3}`

`\sf{ y = 22°}`

Thus, The value of y is 22°

Therefore,

The measurement of Angle HER

`\sf{ = 5 × 22 - 26 }`

`\sf{ = 110 - 26 }`

`\sf{\red{= 84° }}`

The measurement of angle HER is 84°

Hence option D is correct

Answer 7 :-

We have,

`\sf{ HZ = 4a - 5 \:and \:RZ = 3a + 5 }`

• The diagonals of parallelogram are equal in length
• Here, RZ is the bisector of diagonal HR

`\sf{ 4a - 5 = 3a + 5 }`

`\sf{ 4a - 3a = 5 + 5}`

`\sf{ a = 10}`

Thus, The value of a is 10

Therefore,

The measurement of HZ

`\sf{ = 4 × 10 - 5 }`

`\sf{ = 40 - 5 }`

`\sf{\red{= 35 \: cm }}`

The measurement of HZ is 35 cm

Hence, Option C is correct

Answer 8 :-

We have ,

One diagonals = 5x - 47

Another diagonal = 2x + 34

• In isosceles trapezoid, Diagonals are equal in length.

From above property,

`\sf{ 5x - 47 = 2x + 34 }`

`\sf{ 5x - 2x = 34 + 47}`

`\sf{ 3x = 81 }`

`\sf{ x = 81/3 }`

`\sf{ x = 27}`

Thus, The value of x is 27

Hence, Option A is correct

Answer 9 :-

We have,

The sides of parallelogram GAME are (7x - 1 ) , ( 5x + 10 ) , (6x) , ( 7x - 2 )

• In parallelogram, Opposite sides are equal

From above property,

`\sf{ 7x - 1 = 6x }`

`\sf{ 7x - 6x = 1 }`

`\sf{ x = 1 }`

`\sf{ 5x + 10 = 7x - 2}`

`\sf{ 7x - 5x = 10 + 2 }`

`\sf{ 2x = 12}`

`\sf{ x = 12/2 }`

`\sf{ x = 6 }`

Thus, measurements of parallelogram GAME in inches is 1 and 6 .

Hence, Option B is correct

Answer 10 :-

We have,

`\sf{ ES = 18 cm}`

• The diagonals of rectangle are equal in length.
• Here, NP = OE
• PS and NS act as a bisector in OE and OS and ES act as a bisector in NP

From above we can say that,

`\sf{ OE = OS + ES }`

`\sf{ OE = 2ES ( OS = ES bisector}`

`\sf{ OE = 2 × 18 }`

`\sf{ OE = 36cm }`

Thus, The value of OE is 38 cm

Therefore,

`\sf{ OE = NP }`

[ Diagonals of the given rectangle ]

`\sf{\red{NP = 36 cm }}`

Thus , The value of NP is 36 cm

Hence, Option C is correct