Question

In the given isosceles triangle ABC, find the measure of the vertex angle and base angles b=x+42 c=3x​

Answer 1

Step-by-step explanation:

1.

x+42 = 3x ( since AB = AC from the fig)

3x-x = 42

2x = 42

x = 21

angle C = 3x = 3×21 = 63

angle B = angle C ( isosceles triangle)

angle A = 180 - (63 + 63)

= 180 - 126

= 54

2. AC = BC

Hence Angle A = Angle C = 30

therefore angle ACB = 180 - (30 + 30)

= 180 - 60

= 120

angle ECD = angle ACB ( vertically opposite angles)

therefore, angle ECD = 120

Answer 2

Answer:

x=27,b=69,c=91

Step-by-step explanation:

from fig angle of A=30

and triangle ABC is isosceles triangles and has two equal angles and sides ,so angle B=angle C

so by Angle Sum Property

sum of all angles of a triangle is 180

so Angle A+Angle B+AngleC=180

30+x+42+3x=180

72+4x=180

4x=180_72

4x=108

x=108÷4

x=27

so,b=x+42=69

and c=3x=91