plz solve this question @tennitrij86
Answers
Answer:
d is 108°
Step-by-step explanation:
being parallel
Step-by-step explanation:
Solution :-
a)
From the figure,
72° and d are vertically opposite angles which are equal.
=> d = 72°
and
c and 72° are linear pair
=> c+72° = 180°
=> c = 180°-72°
=> c = 108°
Therefore,
c = 108°
d = 72°
b)
From the figure,
b and 97° are linear pair
=> b+97° = 180°
=> b = 180°-97°
=> b = 83°
and
a and b are interior angles on the same side to the transversal which are supplementary
=> a+b = 180°
=> a+83° = 180°
=> a = 180°-83°
=> a = 97°
or
a and 97° are corresponding angles which are equal
=> a = 97°
and
a and c are are linear pair
=> a+c = 180°
=> 97°+c = 180°
=> c = 180°-97°
=> c = 83°
Therefore,
a = 97°
b = 83°
c = 83°
c)
From the figure,
c and 135° are vertically opposite angles which are equal.
=> c = 135°
and
c and d are are linear pair
=> c+d = 180°
=> 135°+d = 180°
=> d= 180°-135°
=> d = 45°
a and c are corresponding angles which are equal
=> a = c
=> a = 135°
b and d are alternative interior angles which are equal
=> b = d
=> b = 45°
and
f and 52° are corresponding angles which are equal
=> f = 52°
and
e and f are linear pair
=> e+f = 180°
=> e+52° = 180°
=> e = 180°-52°
=> e = 128°
Therefore,
a = 135°
b = 45°
c = 135°
d = 45°
e = 128°
f = 52°
d)
From the figure,
a and 135° are interior angles on the same side to the transversal which are supplementary
=> a+135°= 180°
=> a = 180°-135°
=> a = 45°
and
b and 59° are alternative interior angles which are equal
=> b = 59°
Now,
a+b = 45°+59° = 104°
We know that
The sum of all angles around a point is 360°
=> a+b+c = 360°
=> 104°+c = 360°
=> c = 360°-104°
=> c = 256°
Therefore,
a = 45°
b = 59°
c = 256°
e)
From the figure,
a and 60° are exterior angles on the same side to the transversal which are supplementary.
=> a+60°= 180°
=> a = 180°-60°
=> a = 120°
and
c and 60° are interior angles on the same side to the transversal which are supplementary
=> c+60°= 180°
=> c = 180°-60°
=> c = 120°
and
c and d are linear pair
=> c+d = 180°
=> 120°+d = 180°
=> d = 180°- 120°
=> d = 60°
b and d are interior angles on the same side to the transversal which are supplementary
=> b+d= 180°
=> b+60° = 180°
=> b = 180°-60°
=> b = 120°
Therefore,
a = 120°
b = 120°
c = 120°
d = 60°
Used formulae:-
If two parallel lines Intersected by a transversal then
→ Vertically Opposite angles are equal.
→ Alternative interior angles are equal.
→ Interior angles on the same side to the transversal are supplementary.
→ Exterior angles on the same side to the transversal are supplementary.