Step 1: Concept
Triangle SRT is an isosceles triangle with equal base angles a = b
Triangle TUV is an equilateral triangle with all angles equal: g = d = h
Step 2: Apply sum of angles in a triangle theorem to find angle a and b.
[tex]\begin{gathered} a+b+c=180^o \\ c=40^o \\ \text{Let a = b = x} \\ \text{Therefore} \\ x\text{ + x + 40 = 180} \\ 2x\text{ = 180 - 40} \\ 2x\text{ = 140} \\ x\text{ = }\frac{140}{2} \\ x\text{ = 70} \\ a\text{ = 70 and b = 70} \end{gathered}[/tex]
Step 3:
2) a = 70
3) b + c = 70 + 40 = 110
Step 4:
Since WT is a bisector of angle STV,
Angle f = e = x
b + f + e = 180 sum of angles on a straight line.
b = 70
70 + x + x = 180
2x = 180 - 70
2x = 110
x = 110/2
x = 55
Hence, f = 55
4) f = 55
5) f + b = 55 + 70 = 125
Step 5:
Since triangle TUV is an equilateral triangle, angle g = h = d = 60
g = 60
h = 60
d = 60
6) Angle a + d = 70 + 60 = 130
7) e + g = 55 + 60 = 115
