Question

point X Y and Z in the given figure and show that ∆ABC is isosceles ​

Answer 1

Answer:

Given:- ∆ABC is a isosceles ∆, angle B= 30°, angle BAD = 10°, angle DAE = 50°, angle EAC = 60°

Find that:- angle x,y and z

proof:- given that

In a ∆ABC

AB=AC

angle BAE = angle BAD+angle DAE

angle BAE= 60°

angle BAE=angle CAE {angle CAE= 60°

In ∆BAE and ∆CAE

AB = AC {given

angle BAE=angle CAE {angle are equal

AE = AE

So, that SAS congruence criterion

∆BAE = ∆CAE

by CPCT

BE= CE (i)

angleAEB = angleAEC (ii)

angle ABE = angle ACE (iii)

by (iii)

angleABE = angleACE

angleACE = 30° {angleABE= 30°

z = 30°

In ∆AEC all angles sum

angleA+angleE+angleC = 180°

60°+30°+angleE=180°

angleE= 180°-90°

angleE = 90°

y = 90°

In ∆ DAE all angles sum

angle D+angle A+angle E = 180°

angle D+50°+90°=180°

angle D=180°-140°

angle D= 40°

x = 40°

Hence, the value of x,y and z is 40°,90° and 30°.