Question

What is the value of x?

Answer 1

98°

Step by step Step-by-step explanation :

As we can see in figure,

∠F = 53°

∠H = 45°

So,

`\:\mathsf{∠FGH\: +\: ∠GHF \:+ \:∠HFG\: = \:180°}`

[Angle sum property, which states that the sum of all the angles of a triangle is 180°]

=> ∠FGH + 45° + 53° = 180°

=> ∠FGH = 180° - 98°

=>
`\:\bf\boxed{∠FGH\: =\:82°}`

Now,

∠x + ∠FGH = 180°

[linear pair]

=> ∠x = 180° - 82°

=>
`\:\bf\boxed{∠x\: =\:98°}`

Alternative Method :

We know that sum of two opposite interior angles is equal to the exterior angle.

So

∠x = ∠GHF + ∠HFG.

=> ∠x = 45 ° + 53°

=>
`\:\bf\boxed{∠x\: =\:98°}`

Hope this helps!