Answer: a. x = 15, y = 40
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