Question

9 class-MATHS
LINES AND ANGLES
RD SHARMA
SOLVE THIS!!
MATHS ARYABHATTA,GIVE A GLANCE ON IT.
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Answer 1

Answer:

Angle HKL=85°

Step-by-step explanation:

if AB||CD||EF

So,

angleKHD=angle BKL=25°

angle CHG=angle KHC=60°

Now

Angle HKL=AngleBKL+AngleCHK

= 25°+60°=85°

Answer 2

$\large{\boxed{\boxed{\sf{ANSWER}}}}$

∠HKL = 145°

$\large{\boxed{\boxed{\sf{SOLUTION}}}}$

Extend LK to meet line GF at point N.

From figure, CD || GF,

so we know that,

alternate angles are equal.

• ∠CHG =∠HGN = 60°

Corresponding angles of parallel lines are equal

• ∠HGP =∠KNF = 60°

Linear pair

• ∠KNG =180° - ∠KNF

→ ∠KNG =180° - 60

→ ∠KNG = 120°

Corresponding angles of parallel lines are equal

• ∠GNK = ∠AKL= 120°

alternate angles of parallel lines are equal

• ∠AKH = ∠KHD = 25°

So,

• ∠HKL = ∠AKH + ∠AKL

→ ∠HKL = 25° + 120 °

→ ∠HKL = 145°

[ Note - SEE THE ATTACHMENT ]