Question

please answer ... find x,y and z

Answer 1

Heya!

In triangle ABD,

By angle sum property,

angle ABD + angle ADB + angle BAD = 180

=) 30 + angle ADB + 10 = 180

=) angle ADB = 180 - 40

=) angle ADB = 140°

_____________________

angle ADB + angle ADE = 180 ( linear pair)

=) 140 + angle ADE = 180

=) x = 40 °

_______________________


In triangle ADE,

=) angle ADE + angle AED + angle DAE = 180

=) 40 + angle AED + 50 = 180

=) angle AED + 90 = 180

=) angle AED = 90°

________________________

angle AED + angle AEC = 180 ( linear pair)

=) 90 + y = 180

=) y = 90°

_________________________

In triangle AEC,

angle AEC + angle ACE + angle EAC = 180

=) y + z + 60 = 180

=) 90 + z + 60 = 180

=) z = 180 - 150

=) z = 30 °

Hence, x = 40°

y = 90°

z = 30°

Then,

angle ABC = angle ACB = 30°

Since, if base angles are equal then , the triangle is isosceles triangle.

Hence, Triangle ABC is an isosceles triangle.

Hope it helps u.