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Answer:
x=102 degree; y=88 degree
Step-by-step explanation:
PBO=72 degree(let the point between AB be O)
We know,
POB+POA= 180 degree
=72 degree + POA=180 degree
=POA=180-72
=108 degree
Now,
we know POA=POE(let the other point between CD be E)
=108=40+ the other
the other angle=108-40
the other angle=64
Now,
64+24+x=180(as it is a triangle)
x=180-88
x=102 degree
We also know
24+y=108 degree
y=108-24
y=88 degree
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Answer:
x=88
y=84
Step-by-step explanation:.
As we know AB is parallel to CD and PQ is the transversal.
Now we know that
1. Vertically opposite angles are equal
2. Two adjacent angles on the same line sum up to 180°
Now let's name the co-ordinates of the triangle as LMN
As we know the sum of angles of a triangle = 180°
So to find x we need to find angle L.
And for that we need to apply this property
Two adjacent angles on the same line sum up to 180°
So for that we know that 72+40+Angle L=180°
112+L=180°
L=180-112
L=68
So apply the angle sum property of a triangle we get
68+24+Angle M=180°
92+M=180°
M=180-92
M=88
M=x=88
So here we get x=88
Now to find y
We need to use the properties of angles in parallel lines
The one we will use is the opposite angles sum up to 180°
So we know that 72°+24°+y=180°
96°+y=180°
y=180-96°
y=84°