Question

Please solve this... fast....​

Answer 1

Answer:

question 1)

GIVEN :

∠ABC = 80°

∠CFH = 45°

∠CHF = 35°

TO PROVE : l║m

PROOF :

∠CFH + ∠FHC + ∠HCF = 180 °      (angle sum property)

45° + 35° + ∠HCF = 180°

80° + ∠HCF = 180°

∠HCF = 180° - 80°

∠HCF = 100°

Now , ∠HCF +∠ECH = 180°                 (linear pair)

∠ECH + 100° = 180°

∠ECH = 180° - 100°

∠ECH = 80°                                ...........(equation 1)

Also ∠ECH , ∠ABC  are corresponding angles

∠ECH = 80°                   ..............(equation 1)

∠ABC = 80°                   ..............(given)

⇒∠ECH = ∠ABC

∵corresponding angles are equal

∴ l ║ m   (as corresponding angles of parallel lines are equal)

question 2)

GIVEN :

PQ ║ RS

∠UTR = y

∠TRS = 110°

∠TPQ = 35°

TO FIND :

y

CONSTRUCTION :

Extend line RS so that it meets PT at point U

PROOF :

∵ RS ║ PQ

∴ SU ║ PQ

⇒ ∠TUR = ∠TPQ                  (corresponding angles are equal)

⇒∠TUR = 35°

Now , ∠TRS + ∠TRU = 180°              (linear pair)

∠110° + ∠TRU = 180°

∠TRU = 180° - 110°

∠TRU = 70°

Also , ∠UTR + ∠TRU + ∠TUR = 180°                (angle sum property)

∠UTR + 70° + 35° = 180°

∠UTR + 105° = 180°

∠UTR = 180° - 105°

∠UTR = 75°

∵∠UTR = y                           (given)

⇒ y = 75°          

I hope this helps...........