Question

l is parallel to m and n is transversal. if angle b=(3x -10 )and angle h =(5x -30) then determine all the angles

Answer 1

angle b = d (vertically opposite angle)
so d = (3x-10)
same angle h= f ( vertically opposite angle)
but angle d = f (alternate interior angle)
so ( 3x-10) = (5x -30)
= 3x-10= 5x -30
3x- 5x = -30+10
-2x = -20
x = -20/-2
x =10

Answer 2

Answer:

∠b=∠d=∠h=∠f=20°

∠a=∠c=∠g=∠e=160°

Step-by-step explanation:

∠h=∠d (corresponding angles)

∠d=5x-30

∠d=∠b

5x-30=3x-10

5x-3x= -10+30

2x=20

x=20/2=10

∠b=3x-10                                            

∠b=3×10-10

∠b=20°

∠h=5x-30

∠h=5×10-30

∠h=20°

∠b=∠d (vertically opposite angles)

∠d=20°

∠d=∠f (alternate interior angles)

∠f=20°

∴∠b=∠d=∠h=∠f=20°

∠a+∠b=180 (linear pair)

∠a+20=180

∠a=180-20=160°

∠a=∠c (vertically opposite angles)

∠c=160°

∠c=∠g (corresponding)

∠g=160°

∠g=∠e (vertically opposite angles)

∠e=160°

∴∠a=∠c=∠g=∠e=160°