Question

Please Solve this :-​

Answer 1

Answer:

m∠ABC = 130° , m∠BCD = 120°

Step-by-step explanation:

given :

AD || BC , m∠DAP = 25° & m∠ADP = 30°

AP & DP are bisectors of ∠A & ∠B respectively.

to find :

m∠ABC & m∠BCD

solution :

m∠A = 2 × m∠DAP .........

bisector of devides angle equally

:. m∠A = 2 × 25° = 50°

m∠D = 2 × m∠ADP .........

bisector of devides angle equally

:. m∠D = 2 × 30° = 60°

here AD || BC & AB is transversal ,

m∠A + m∠B = 180° ......interior angles theorem

50° + m∠B = 180°

:. m∠B = 180° - 50° = 130°

here AD || BC & CD is transversal ,

m∠C + m∠D = 180° ......interior angles theorem

50° + m∠C = 180°

:. m∠B = 180° - 60° = 120°

hence proved.