In the figure, ∠4 is an exterior angle to aul.

a) explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

b) what is m∠4?

*i'm not good at these types of problems, i have a hard time trying to figure out where to start*

a) see explanation below.

b) measure of ∠4 =  77°.

Step-by-step explanation:

Given a figure ∠4 is an exterior angle to ΔAUL.

a) We have to explain  why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

That is why ∠4 = ∠1 +∠2

Lets first  ∠1 +∠2 = 52° +25° = 77°

angle sum property of triangle states that the sum of angles of a triangle is always equal to 180°.

Thus, ∠1 +∠2 + ∠3 = 180°

Substitute the know value and find the angle 3.

⇒ 77° + ∠3 = 180°

⇒ ∠3 = 180° - 77° = 103°

Also ∠3 + ∠4 = 180° (Linear pair )

⇒ ∠4 = 180° - 103° = 77°.

⇒ ∠4 = ∠1 +∠2

Thus, ∠4 is equal to the sum of the measures of the two nonadjacent interior angles.

b) Measure of ∠4 =  77°.

  the center (h, k) is (-2, 3), and the radius r is 3

Step-by-step explanation:

Separate the x- and y-terms and complete the square for each. The square is completed by adding the square of half the linear term coefficient.

  (x^2 +4x +(4/2)^2) +(y^2 -6y +(-6/2)^2) = -4 +(4/2)^2 +(-6/2)^2

  (x +2)^2 +(y -3)^2 = 9

Compare to the form ...

  (x -h)^2 +(y -k)^2 = r^2

and you see that the center (h, k) is (-2, 3), and the radius r is 3.