Question

find the value of x in the following figure
please full answer​

Answer 1

85+ 44=180

129=180

x= 180- 129

x = 51

Answer 2

Answer:

Value of x is 51°.

Step-by-step explanation:

Suppose O is point at which line MQ and NP are intersecting.

Given that,

• ∠NMO is 85°.
• ∠QOP is 44°.
• MO = OQ.
• NO = OP.

In ∆MON and ∆QOP :

◍ MO = OQ [Given]

◍ NO = OP [Given]

◍ ∠MON = ∠POQ = 44° [By vertically opposite angle property which means when two lines are intersecting at any point then vertically opposite angles are equal].

By SAS (Side Angle Side) congruence rule :

∆MON is congruent to ∆QOP.

By CPCT :

∠NMO = ∠OQP = 85° ----(1)

Now,

We know,

✿ Sum of all interior angles of triangle is equal to 180°. This property is also known as "Angle sum property of triangle".

So,

$\implies$ ∠OQP + ∠POQ + x = 180°

• Put ∠OQP = 85° [By equation (1)] and ∠POQ = 44°

$\implies$ 85° + 44° + x = 180°

$\implies$ 129° + x = 180°

$\implies$ x = 180° - 129°

$\implies$ x = 51°

Therefore,

Value of x is 51°.