please solve it step by step
Answers
Answer:
here mark me as brailiest
Answer:
Step-by-step explanation:
Two parallel lines l and m be cut a transversal t, forming angles.
It is given that ∠1:∠2=5:7
Let the measures of angles by 5x and 7x,
Then,
5x+7x=180
12x=180
x=180/12
x=15
∴∠1=5x=5×15=75
o
∠2=7x=7×15=150
o
We know that,
∠2+∠3=180
o
[∵ linear pair]
150
o
+∠3=180
o
=∠3=180−105
∠3=75
o
∠3+∠6=180
o
[∵ the sum of the consecutive interior angles is 180
o
]
75
o
+∠5=180
o
∠6=180−75
∠6=150
o
Now ∠6=∠8=150
o
[∵ vertically opposite angles are equal]
∴∠1=75
o
,∠2=105
o
,∠=75
o
and ∠8=105
o
.L1 & L2 are in ratio 1:2
letL1=k
L2=2k
L1+L2=180
∘
(∵sum of angles on a straight line=180
∘
)
⟹k+2k=180
∘
⟹3k=180
∘
⟹k=60
∘
⟹L1=60
∘
,L2=120
∘
L2+L3=180
∘
(sum of angles on a straight line=180
∘
)
⟹L3+120
∘
=180
∘
⟹L=60
∘
L3=L7(∵l& m are parallel ∴ corresponding angles)
L7=60
∘
Angle 1 + Angle 2 = 180 degrees;
5x + 7x = 180 ;
12x = 180;
x = 15 degrees
Angle 1 = Angle 3 = 5x = 5*15 = 75 degrees;
Angle 2 = Angle 8 = 7x = 7*15 = 105 degrees