Question

SHow your work please. Ill give you all of the points I have.

Answer 1

130=54+4y

130-54=4y

y=76/4

y=19°

54+76+2x=180

130+2x=180

2x=50

x=25

y=19° and x=25°

Answer 2

x = 25°

y = 19°

Explanation:

Exterior angle of a triangle:

An exterior angle of a triangle is an angle that is formed by one side of the triangle and the extension of another side of the triangle.

Every exterior angle of a triangle is equal to the sum of the two remote interior angles.

In this case: we can say that

130° is an exterior angle and 54° and 4y° are remote interior angles.

So,

130° = 54° + 4y°

Subtract 54° on both sides:

130° - 54° = 54° + 4y° - 54°

76° = 4y°

Divide both sides by 4.

`\sf (4y^\circ)/(4) =(76^\circ)/(4)`

y = 19°

we have

Linear pair:

A linear pair is a pair of angles that are supplementary, meaning that their measures add up to 180 degrees.

In this case:

130° and 2x° are linear pair.

So,

130° + 2x° = 180°

Subtract 130° on both sides:

130° + 2x° - 130° = 180° - 130°

2x° = 50°

Divide both sides by 2.

`\sf (2x^\circ)/(2) =(50^\circ)/(2)`

x = 25°

Therefore, value of x is 25° and y is 19°.