Find the unknown values x and y in the following diagram.
Answers
Answer:
Y=80(vertically opposite angles)
x=50(sum of all angle of a triangle is 180)
Answer:
PPankaj Sanodiya
i) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle.
50^0+x=120^0
x=120^0-50^0
x=70^0
Now, As we know the sum of internal angles of a triangle is 180. so,
50^0+x+y=180^0
50^0+70^0+y=180^0
y=180^0-50^0-70^0
y=60^0
Hence, x=70^0\:\:and\:\:y=60^0.
ii) As we know when two lines are intersecting, the opposite angles are equal. So
y=80^0
Now, As we know the sum of internal angles of a triangle is 180. so,
50^0+y+x=180^0
50^0+80^0+x=180^0
x=180^0-50^0-80^0
x=50^0
Hence, x=50^0\:\:and\:\:y=80^0.
iii) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle
x=50^0+60^0
x=110^0
Now, As we know the sum of internal angles of a triangle is 180. so,
y+50^0+60^0=180^0
y=180^0-50^0-60^0
y=70^0
Hence, x=110^0\:\:and\:\:y=70^0.
iv)
As we know when two lines are intersecting, the opposite angles are equal. So
x=60^0
Now, As we know the sum of internal angles of a triangle is 180. so,
30^0+y+x=180^0
30^0+y+60^0=180^0
y=180^0-30^0-60^0
y=90^0
Hence, x=60^0\:\:and\:\:y=90^0
v) As we know when two lines are intersecting, the opposite angles are equal. So
y=90^0
Now, As we know the sum of internal angles of a triangle is 180. so,
y+x+x=180^0
90^0+2x=180^0
2x=90^0
x=45^0
Hence, x=45^0\:\:and\:\:y=90^0
vi)As we know when two lines are intersecting, the opposite angles are equal. So
y=x
Now, As we know the sum of internal angles of a triangle is 180. so,
x+x+x=180^0
3x=180^0
x=60^0
Hence, x=60^0\:\:and\:\:y=60^0.
Step-by-step explanation:
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