Question

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Answer 1

Answer:

x = 11

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Angle ABC is an exterior angle of the triangle.

Angles D and C are its remote interior angles.

m<ABC = m<D + m<C

12x - 2 = 57 + 7x - 4

Combine like terms on the right side.

12x - 2 = 7x + 53

Subtract 7x from both sides.

5x - 2 = 53

Add 2 to both sides.

5x = 55

Divide both sides by 5.

x = 11

Answer: x = 11

Answer 2

Answer:

According to exterior angle property, one of the exterior angles of a triangle is equal to the sum of the opposite 2 interior angles.

Thus,

12x-2= 57+7x-4

= 12x = 57-4+7x

= 12x = 53+7x

= 53= 7x-12x

= 53=-5x

= 53÷-5=x

= x= 10.6

Thus x= 10.6