Find the value of x: ( give reasons to support your answers)
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Answers
↬As in figure we can see that there is a two wide line in both side it represents that both the sides on which the wide line are there are equal.
★Coming on figure :-1
⇛Here two sides are equal .Therefore their angles are also equal ( angles opposite to equal sides are equal )
Now In the given triangle
One angle is given which is 40⁰ and that angles is equal to its another corresponding angle so, Now we have two angles of 40⁰
By angle sum property
40⁰+40⁰+x =180⁰
x=180⁰-80⁰
x=100⁰
★Coming on figure :-2
⇛As it is given that in a both triangle there is two equal corresponding sides , Now taking we will do congruent to both triangles by AAA congruence
Therefore there corresponding angles of both the triangle will be equal
X=50⁰
★Coming on figure:-3
⇛We will se in this figure that two sides are equal .
Therefore its corresponding sides will be equal ,Now x⁰=x⁰
By angle sum property
x+x+80⁰=180⁰
2x=180⁰-80⁰
x=100⁰/2
x=50⁰
★Coming on figure:-4
⇛As there is 1 exterior angle which lies on straight line. So by using linear pair we will get internal angle of the triangle
↬Required interior angle +130⁰=180⁰
↬Required interior angle of triangle =50⁰
As we will again see that there is two sides equal , So their angle will also be equal .
Now,
By angle sum property
50⁰+50⁰+x=180⁰
x=180⁰-100⁰
x=100⁰