The values of x and y in the figure is below;
3. x = 36
4. y = 48°
5. x = 48
6. y = 5
7. x = 27.8
8. y = 35
What is the value of x and y in the figure?
3.
From triangle ABC
108° + 48° + ∠A = 180°
156° + ∠A = 180°
∠A = 180° - 156°
∠A = 24°
If ∆ABC ≅ ∆FDE
Then
∠B ≅ ∠D
48° = y°
4.
Also,
∠A ≅ ∠F
24° = (2x - y)
24 = 2x - 48
24 + 48 = 2x
72 = 2x
Divide both sides by 2
x = 72/2
x = 36
5.
polygon ABCD ≅ PQRS
∠A = ∠P
2x + 4 = 100
2x = 100 - 4
2x = 96
Divide both sides by 2
x = 48
6.
Also
CD = RS
3y - 3 = 12
3y = 12 + 3
3y = 15
Divide both sides by 3
y = 15/3
y = 5
7.
∆ABC ≅ ∆DEF
∠A = ∠P
65° = (2y - 5)°
65 = 2y - 5
Add 5 to both sides
65 + 5 = 2y
70 = 2y
Divide both sides by 2
y = 70/2
y = 35
8.
BC = EF
90.6 = 2x + y
90.6 = 2x + 35
Subtract 35 from both sides
90.6 - 35 = 2x
55.6 = 2x
Divide both sides by 2
x = 55.6/2
x = 27.8
Therefore, the value of x and y in the third figure is 27.8 and 35 respectively.