In the figure given below, a transversal 'p' cuts two parallel lines 'l' and 'm' respectively. If ∠1 = 65°, find all the other angles.
Answers
Answer:
Step-by-step explanation:As per the diagram
We know that when a line is intersected by a transversal then
Corresponding angles are equal
Alternate interior angles are equal
Vertically opposite angles are equal
and also Sum of all the angles in a straight line is 180
o
Given,
∠CMQ=60
o
=>∠LMD=60
o
[ ∵ vertically opposite angles are equal]
=>∠QMD=180−60
o
[ ∵sum of angles in a straight line is 180
o
]
∴ ∠QMD=120
o
=>∠CML=120
o
[ ∵ vertically opposite angles are equal]
=>∠MLB=120
o
[ ∵ Alternate interior angles are equal]
=>∠LMD=MLA=60
o
[ ∵ Alternate interior angles are equal]
∴ ∠MLA=PLB=60
o
[ ∵ vertically opposite angles are equal]
=>∠MLB=∠ALP=120
o
[ ∵ vertically opposite angles are equal]
∴ ∠CMQ=60
o
, ∠QMD=120
o
, ∠CML=120
o
, ∠LMD=60
o
,
∠MLA=60
o
, ∠MLB=120
o
, ∠ALP=120
o
and ∠PLB=60
o
.
- ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 ( The pairs of corresponding angles)
- ∠2 and ∠8, ∠3 and ∠5 (The pairs of alternate interior angles)
- ∠2 and ∠5, ∠3 and ∠8 (The pairs of interior angles on the same side of the transversal)
- ∠1 and ∠3, ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8 (The vertically opposite angles)