30 points! (check image) a. x = 15, y = 40
b. x = 30, y = 40
c. x = 15, y = 20
d. x = 30, y = 20

a. x = 15, y = 40

Step-by-step explanation:

So we already know that ΔABC and ΔFDE are congruent, which means their angles are equal. Based on this information, we could note that:

∠A = ∠F

∠C = ∠E

∠B = ∠D

Since we already know the measurement of ∠B, we could then conclude that ∠D, or y, is equal to 40°. This leaves us with two possible answers, a or b.

In order to find the value of x, we need to know the measurement of ∠F. And in order to find ∠F, we need to find the measurement of ∠A. We already know that the angles in a triangle sums up to 180°. So we would start as the following.

∠A + ∠B + ∠C = 180

We first substitute the known measurements.

∠A + 40 + 110 = 180

We then add up 40 with 110.

∠A + 150 = 180

We finally substract 150 on both sides of the equation. This gives us the measurement of ∠A.

∠A = 30°

Now that we know ∠A, we could start finding the value of x. So we already know this:

∠A = ∠F

We first substitute each angle with their known measurements.

30 = 2x

We now divide both sides by two. This gives the value of x.

x = 15

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x