Question

Please answer the question in the attachment. Plzz fast.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

C. 66° and 48°

Step-by-step explanation:

We need to identify the relevant triangles in the picture and use the properties of a triangle and linear angle to solve the problem.

Let's begin by solving the x first as it is fairly easy.

Consider the triangle TCE. We already know that the sum of all angles of a triangle is 180. So, ∠TCE+∠CET+∠ETC = 180

Putting the known values we get;

35 + 31 + ∠ETC = 180

∠ETC = 180-66 = 114

Now, let's consider the line CTA. Being a straight line ∠CTA = 180

We also know that ∠CTE + ∠ETA = ∠CTA

So, 114 + x = 180

x = 180-114 = 66

Now consider the triangle SBD.

∠SBD + ∠BDS + ∠DSB = 180

Putting the values,

30 + 36 + ∠DSB = 180

∠DSB = 180-66 = 114

Now let us consider the triangle ATS with side AS extended till D.

We can observe that ∠TSD is an exterior angle of the triangle.

Hence  ∠SAT + ∠ATS = ∠TSD

Also ∠TSD = ∠BSD (which is already found in previous step)

∴ y + x = ∠BSD Now putting the values we get;

y + 66 = 114

Hence, y = 114-66 = 48

∴ x = 66° and y = 48°