Question

ᴘʟᴇᴀsᴇ sᴏʟᴠᴇ ɪᴛ ғᴀsᴛ.
ᴅᴏɴ'ᴛ ᴅᴀʀᴇ ᴛᴏ sᴘᴀᴍ.​

Answer 1

$\huge\red{Answer}$

Q.1.

PQRS is a quadrilateral  in which diagonal PR and QS intersect at a O .  

to prove - PQ +QR +RS+SP < 2 ( PR + QS )  

proof -

      we know that sum of any two side of a triangle is greater than the third side .

.'. in Δ PQO ,  

      PO+QO>PQ ,  .......................(i)

   in Δ SOP  

       SO + PO >PS , .........................(ii)

  in Δ SOR  

      SO + OR > RS  ...........................(iii)

  in Δ QOR ,  

    QO + OR > QR ...........................(iv)

on adding eqn. i , ii , iii & iv  

   we get ,

PO+QO+SO+PO+SO+OR+QO+OR > PQ+PS+SR+QR  

also ⇒ 2 ( PO + QO + SO + OR ) > PQ+PS+SR + QR  

      = 2( PR + QS ) > PQ+PS+RS + QR  ( proved) ....

Q.2.

(i)The sum of 3 times n and seven is 1.

(ii)subtracting 5 from x gives 8

(iii)subtracting 3 from 1/5 of n gives 6

Q.3.

The first thing we need to do is distribute the -2(1-x) we do this by multiplying the -2 by both 1 and -x.

-2*1=-2

-2*-x=2x

Now we can put them in our problem:

3-5x+2x=-2-2+2x

We are going to put our x's on the left side now:

3-5x+2x-2x Remember, when the x's or numbers cross the equals sign, change the sign!

Now we are going to put the numbers in the right side:

-5x+2x-2x=-3-2-2

Combine like terms:

-5x=-7

Finally, divide both sides by -5

x= -7/-5

Remember, if both numbers in a fraction or negative, it is a positive fraction

Final Answer: [x= 7/5]

Q.4.

(i)

triangle APB

angle sum property = 180

angle A + Angle P + z=180

100+50+z=180

150+z=180

z=30

100+y = 180 (straight line is 180 )

y =80

TRIANGLE ABC

ANGLE A +ANGLE B+ ANGLE C =180 (ANGLE SUM PROPERTY)

Y+X+75 =180

80+X +75 =180

155+X =180

X=180-155

X=25

X=25

Y=80

Z=30

(ii)

angle BAC = angle FAE (vertically opp. angle)

angle BAC = x = 70°

angle BCA + angle ACD = 180° (linear pair)

z + 110 = 180°

angle BCA = z = 70°

angle BCA + angle ABC + angle BAC = 180° ( sum of angles of a triangle is equal to 180°)

z + y + x = 180°

70° +70° +y = 180°

angle ABC = y = 40 °

x = 70°

y = 40°

z = 70°

$\huge\green{hope\;it\;helps}$

$\huge\orange{mark \;as \;brainliest\;}$

Answer 2

Answer:

Q.1.

PQRS is a quadrilateral in which diagonal PR and QS intersect at a O .

to prove - PQ +QR +RS+SP < 2 ( PR + QS )

proof -

we know that sum of any two side of a triangle is greater than the third side .

.'. in Δ PQO ,

PO+QO>PQ , .......................(i)

in Δ SOP

SO + PO >PS , .........................(ii)

in Δ SOR

SO + OR > RS ...........................(iii)

in Δ QOR ,

QO + OR > QR ...........................(iv)

on adding eqn. i , ii , iii & iv

we get ,

PO+QO+SO+PO+SO+OR+QO+OR > PQ+PS+SR+QR

also ⇒ 2 ( PO + QO + SO + OR ) > PQ+PS+SR + QR

= 2( PR + QS ) > PQ+PS+RS + QR ( proved) ....

Q.2.

(i)The sum of 3 times n and seven is 1.

(ii)subtracting 5 from x gives 8

(iii)subtracting 3 from 1/5 of n gives 6

Q.3.

The first thing we need to do is distribute the -2(1-x) we do this by multiplying the -2 by both 1 and -x.

-2*1=-2

-2*-x=2x

Now we can put them in our problem:

3-5x+2x=-2-2+2x

We are going to put our x's on the left side now:

3-5x+2x-2x Remember, when the x's or numbers cross the equals sign, change the sign!

Now we are going to put the numbers in the right side:

-5x+2x-2x=-3-2-2

Combine like terms:

-5x=-7

Finally, divide both sides by -5

x= -7/-5

Remember, if both numbers in a fraction or negative, it is a positive fraction

Final Answer: [x= 7/5]

Q.4.

(i)

triangle APB

angle sum property = 180

angle A + Angle P + z=180

100+50+z=180

150+z=180

z=30

100+y = 180 (straight line is 180 )

y =80

TRIANGLE ABC

ANGLE A +ANGLE B+ ANGLE C =180 (ANGLE SUM PROPERTY)

Y+X+75 =180

80+X +75 =180

155+X =180

X=180-155

X=25

X=25

Y=80

Z=30

(ii)

angle BAC = angle FAE (vertically opp. angle)

angle BAC = x = 70°

angle BCA + angle ACD = 180° (linear pair)

z + 110 = 180°

angle BCA = z = 70°

angle BCA + angle ABC + angle BAC = 180° ( sum of angles of a triangle is equal to 180°)

z + y + x = 180°

70° +70° +y = 180°

angle ABC = y = 40 °

x = 70°

y = 40°

z = 70°

thnx for points