The measure of ∠bcd is 120°. the measure of ∠abc is 85°. what is measure of ∠bac? enter your answer in the box. ° a triangle a b c. side a c is the base. a ray extends through vertex c and passes through a point labeled as d.

Explanation:

Here, In ,  Side AC is the base. A ray extends through vertex C and passes through a point labeled as D.

And,   and

Since, is the exterior angle of the

Therefore, by the property of exterior angle,

⇒

7

step-by-step explanation:

the answer would be 7

(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