Question

∆XYZ is an equilateral triangle such that XO bisects ∠X.

Also, ∠XYO = ∠XZO. Show that ∆YXO ≅ ∆ZXO​

Answer 1

Step-by-step explanation:

WE know ∆ PQR ≅ ∆XYZ by ASA congruence.

Therefore ∠Q = ∠Y i.e., x + 15 = 80° and ∠R = ∠Z i.e., 5y + 10 = 30°.

Also, QR = YZ.

Since, x + 15 = 80°

Therefore x = 80 – 15 = 65°

Also, 5y + 10 = 30°

So, 5y = 30 – 10

Therefore, 5y = 20

⇒ y = 20/5

⇒ y = 4°

Therefore, the value of x and y are 65° and 4°.