Question

find x from this figure​

Answer 1

In a triangle sum of there's angles=180°

As xy=xz

thus Angle XYZ= angle XZY

Thu we get,

52+26+x+26+x=180°

104+2x=180

2x=76

x=38°

Answer 2

So I assume the point on XZ drawn from vertex Y as 'P'

Given : ∠YXZ = ∠YXP = 52°

            ∠XYP = 26°

             XY = XZ

Solution :

Consider ΔXYP

∠YPZ is an exterior angle to the ΔXYP

By exterior angle property

∠YPZ = ∠YXP + ∠XYP

          = 52 + 26

          = 78°

In ΔYPZ,

∠YPZ + ∠YZP + ∠ZYP = 180° ⇒ (angle sum property of triangle)

78° + ∠YZP + x° = 180°

∠YZP = (102-x)° ⇒ (1)

But we have XY = XZ

that is, ΔXYZ is isosceles

Hence ∠YZX = ∠XYZ ⇒ (angles opposite to equal sides of an isosceles                                                                                                                    triangle are equal)

that is, ∠YZP = (26+x)° ⇒ (2)

Comparing equations (1) and (2)

102-x = 26+x

2x = 76

x = 38°

HOPE IT HELPS !!