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Step-by-step explanation:

i) Since,

Angles on the same side of a transversal in a parallelogram, there sum is 180° so,

<RGM + <GMA = 180°

=> <RGM = 180° - <GMA

=> <RGM = 180° - 66°

=> <RGM = 114° (Ans)

ii) Since,

Opposite angles of a diagonal as a transversal (here RM) are equal so,

<GRP = <PMA = 32°

As we have <GMA = 66° so,

=> <GMP = <GMA - <PMA

= 66° - 32°

=> <GMP = 34° (Ans)

iii) Since,

Opposite angles of a parallelogram are equal so,

<RGM = <RAM = 114°

As we have <PAM = 41° so,

=> <GAR = <RAM - <PAM

= 114° - 41°

=> <GAR = 73° (Ans)

iv) Since,

We got <PMA = 32° and <PAM = 41°, so by angle sum property of a triangle PMA,

=> <MPA = 180° - 32° - 41°

=> <MPA = 107° (Ans)

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1