In the
given figure, AB||CD and angleMPA = 2 x anglePQD + 24°
Find (a) angleAPQ
(b) angleDQN
Answers
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
.