Explanation:
Given,
- GRAM is a parallelogram
- m<GMA = 66°
- m<GRP = 32°
- m<PAM = 41°
Solutions:
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)