Question

If Angle BTS Angle GHD, BS = 25, TS = 14, BT = 31, GD = 4x - 11, mangle S = 56°, mangleB = 21°, and

mangleH= (7y + 5), find the values of x and y.

Answer 1

Since Angle BTS and Angle GHD are vertical angles and therefore congruent, we have:

mangle S = mangleH

56° = 7y + 5

Subtracting 5 from both sides gives:

51° = 7y

Dividing both sides by 7 gives:

y = 7.25

Now that we know the value of y, we can find the value of x. Since BS and GD are opposite sides of the rectangle, we know that they are congruent. Therefore, we have:

25 = 4x - 11

Adding 11 to both sides gives:

36 = 4x

Dividing both sides by 4 gives:

x = 9.

Therefore, the values of x and y are x = 9 and y = 7.25.