If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below. Find the value of ∠AGE is

Step-by-step explanation:

Find the diagram attached

From the given diagram, since AB is parallel to CD, this means both lines have similar properties.

For the triangle GEF, AFB, ∠GEF = ∠GED - ∠FED

Given ∠GED = 135 and ∠FED = 90

∠GEF = 135-90

∠GEF = 45°

Also, sum of angle in the triangle GEF is 180°, hence;

∠GEF + ∠EGF + ∠GFE = 180°

45°+∠EGF+90° = 180°

∠EGF+135° = 180°

∠EGF = 180-135

∠EGF = 45°

since the sum of angle on the straight line AGF = 180°, then;

∠AGE+∠EGF = 180°

∠AGE+45° = 180°

∠AGE = 180°-45°

∠AGE = 135°

Hence the value of ∠AGE is 135°

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional