*Due tonight, plz help*

Work Shown:

Angle DCA = 15 degrees (given in diagram)

Angle BAC = 15 degrees, since BAC and DCA are alternate interior angles, so they are congruent to one another. This works because AB is parallel to CD.

Ignore point D. Focus on triangle BAC only. Two angles are known: A = 15, B = 153. Solve for angle C

A+B+C = 180

15+153+C = 180

C+168 = 180

C = 180-168

C = 12

For triangle ABC (ignore point D) the angle C is 12 degrees. If D is involved in the diagram, angle BCA is 12 degrees.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240