Question

Seg ab ≅ seg ad, seg bc≅ seg bd, ∠bad=70°, ∠bcd=65°. find the values of x,y, z and p. *​

Answer 1

In △PBC,

PB = PC

∠PBC=∠PCB=x (Isosceles triangle property)

Sum of angle of △PBC,

∠PCB+∠PBC+∠BPC=180

x+x+140=180$

x=20∘

In △ABC,

AB = AC

thus, ∠ABC=∠ACB=z (Isosceles triangle property)

Sum of angles of triangle ABC,

∠ABC+∠ACB+∠BAC=180

z+z+40=180

2z=140

z=70∘

Now, ∠ACP=∠ACB−∠PCB

y=70−20

y=50∘