Question

in the given figure l parallel to m and p parallel to n .If angle 1=75 degree prove that angle 2= angle 1 + 1/3 of a right angle​

Answer 1

Step-by-step explanation:

given that,

l || m

p||n

As two pairs of opposite sides are parallel,the closed figure formed by lines p, n, l, m is, a

parallelogram.

also given that,

angle 1=75°

so,

angle 1 + the inner angle formed by p and l = 180°(linear pair)

75°+inner angle=180°

inner angle =180-75°

inner angle formed by p and l =105°

now, angle 2 is also equal to 105°(opposite angles of a parallelogram are equal).

We have to prove that:-

angle 2=angle 1 +(1/3×90°) -(1)

putting the value of angle 1 and angle 2 in equation(1),

105°=75°+30°

105°=105°

LHS AND RHS ARE EQUAL,

HENCE PROVED

Hope it helps!