Respuesta :

Answer:

x = 4

Step-by-step explanation:

From the figure attached,

Two lines l and m are the parallel lines.

Angle BAD is an exterior angle of triangle ABC.

By the theorem of exterior angle of a triangle,

"Exterior angle of a triangle is equal to the sum of two opposite interior angles."

m(∠BAD) = m(∠ABC) + m(∠BCA)

28x = 16x + 48

28x - 16x = 48

12x = 48

x = 4

Therefore, x = 4 will be the answer.  

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Using tha appropriate triangle theorem, the value of x in the given triangle is 4

Recall the theorem ;

  • "The exterior angle of a triangle is equal to the sum of opposite interior angles".

  • The opposite interior angle = 16x and 48

  • Exterior angle = 28x

Expressing as an equation :

16x + 48 = 28x

Collect like terms

16x - 28x = - 48

-12x = - 48

x = 48/12

x = 4

Therefore, the value of x is 4.

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