2.  Find angles x and y in each figure.

Answers (1)

i) As we know, in an isosceles triangle, two sides and the angles they make with the third side are equal. So,

y+120^0=180^0

y=180^0-120^0

y=60^0

Now,  As we know the sum of internal angles of a triangle is 180. so,

x+60^0+60^0=180^0

x=180^0-60^0-60^0

x=60^0

Hence, x=60^0\:\:and\:\:y=60^0.

ii)  As we know, in an isosceles triangle, two sides and the angles they make with the third side are equal.

AND

the sum of internal angles of a triangle is 180. so,

x+x+90^0=180^0

2x=90^0

x=45^0

Also,

y=180^0-x

y=180^0-45^0

y=135^0.

Hence x=45^0\:\:and\:\:y=135^0.

iii) As we know when two lines are intersecting, the opposite angles are equal. 

And

the sum of internal angles of a triangle is 180. so,

x+x+92^0=180^0

2x=180^0-92^0

2x=88^0

x=44^0

Now, As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle

y=x+92^0

y=44^0+92^0

y=136^0

Hence x=44^0\:\:and\:\:y=136^0.

 

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