Question

find x from the following figure.plzz solve it​

Answer 1

Answer:

49

because MP=PL

thenN=P

Answer 2

find : <MLP= x°=?

In triangle LPN

we have to given that LP =NP

so it is isosceles triangle because two side of triangle are equal

then, <PNL = <NLP( by property of isosceles triangle)

let <PNL = <NLP = y ----------(1)

then, the sum of interior angle of triangle is 180 °

so, <PNL + <NLP + <LPN = 180°

y + y + 82° = 180°

2y + 82 = 180°

2y = 98

y= 98/2 = 49°

from eq.(1)

<PNL = <NLP = 49°

now, <MNL and <PNL form linear pair then,

<MNL + <PNL = 180°

<MNL + 49° = 180°

<MNL = 180°- 49° = 131°

<MNL = 131°

similarly In triangle MNL,

MN=LN so, it is isosceles triangle

then, <NML = <NLM ( property of isosceles triangle)

let , <NML = <NLM = m

the sum of interior angle of triangle is 180°

so, <NML + <NLM + <LNM = 180°

m+ m + 131° = 180°

2m = 180° - 131°

2m = 49°

m= 49/2°

hence, <NML = <NLM = 49/2°

since <MLP = <MLN+ <NLP

x = 49/2° + 49°

x=( 49+98 /2 )°

x= 147/2°

x= 73.5°