Find the value of x in the triangle in the picture.

x = 33

Step-by-step explanation:

since the sum of interior angles of a triangle is 180 so simply add the given angles and make it equal to 180 degrees

x + 114 + 33 = 180

x + 147 = 180

x = 180 - 147

x = 33

to check whether the above value of x is correct simply just put the above value of x in

x + 114 + 33 = 180

33 + 114 + 33 = 180

180 = 180

since both sides are equal so that means the above value of x is correct

unless if u could do my questions, if not i wouldn't want to

(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