Please find the value of x.
Q. In the given figure, find the value of x ?
Dear student,
According to the figure,
In triangle ABC,
angle ABC + angle BAC + angle CAB = 180' (angle sum property)
angle ABC + 34' + 30' = 180'
angle ABC = 180' - 34' + 30'
angle ABC = 116'
Then, we can see that,
angle ABC + angle CBD = 180' (linear pair)
116' + angle CBD = 180'
angle CBD = 180' - 116'
angle CBD = 64'
In triangle EBD, we can see that,
angle EDB + angle DBE + angle BED = 180' (angle sum property)
45' + 64' + angle DBE = 180'
angle DBE = 180' - 45' - 64'
angle DBE = 71'
And now we can identify that,
angle DBE + angle CDE = 180' (linear pair)
71' + x' = 180'
x' = 180' - 71'
x' = 109'
Therefore we have found out that x' = 109'
Hope you have understood!!
Cheers!!
According to the figure,
In triangle ABC,
angle ABC + angle BAC + angle CAB = 180' (angle sum property)
angle ABC + 34' + 30' = 180'
angle ABC = 180' - 34' + 30'
angle ABC = 116'
Then, we can see that,
angle ABC + angle CBD = 180' (linear pair)
116' + angle CBD = 180'
angle CBD = 180' - 116'
angle CBD = 64'
In triangle EBD, we can see that,
angle EDB + angle DBE + angle BED = 180' (angle sum property)
45' + 64' + angle DBE = 180'
angle DBE = 180' - 45' - 64'
angle DBE = 71'
And now we can identify that,
angle DBE + angle CDE = 180' (linear pair)
71' + x' = 180'
x' = 180' - 71'
x' = 109'
Therefore we have found out that x' = 109'
Hope you have understood!!
Cheers!!
- 5
other wise
sum of all angles of an triangle = 180
a + c + cba = 180
34 + 30 +cba = 180
64 + cba = 180
cba = 180 -64
= 116
angle cba + angle cbd =180 ( linear pair)
116 +cbd = 180
cbd = 180 -116
cbd = 64
x = angle cbd + d
x = 64 + 45 ( sum of interior opposite angle is equal to opposite exterior angle )
angle x = 109
sum of all angles of an triangle = 180
a + c + cba = 180
34 + 30 +cba = 180
64 + cba = 180
cba = 180 -64
= 116
angle cba + angle cbd =180 ( linear pair)
116 +cbd = 180
cbd = 180 -116
cbd = 64
x = angle cbd + d
x = 64 + 45 ( sum of interior opposite angle is equal to opposite exterior angle )
angle x = 109
- -1
In triangle ABC
34 + 30 + angle CBA = 180 (angle sum property of a triangle)
64 + angle CBA = 180
angle CBA = 180 - 64
Therefore angle CBA = 116
Angle EBA + Angle EBD = 180 (Linear Pair)
116 + Angle EBD = 180
Angle EBD = 180 - 116
Therefore Angle EBD = 64
In triangle EBD
Exterior angle x = Angle EBD + Angle EDB (exterior angle is equal to the sum of it's two opposite interior angles)
Exterior angle x = 64 + 45
Therefore, Exterior angle x = 109
34 + 30 + angle CBA = 180 (angle sum property of a triangle)
64 + angle CBA = 180
angle CBA = 180 - 64
Therefore angle CBA = 116
Angle EBA + Angle EBD = 180 (Linear Pair)
116 + Angle EBD = 180
Angle EBD = 180 - 116
Therefore Angle EBD = 64
In triangle EBD
Exterior angle x = Angle EBD + Angle EDB (exterior angle is equal to the sum of it's two opposite interior angles)
Exterior angle x = 64 + 45
Therefore, Exterior angle x = 109
- 2
According to the question
∆ABC =A-34°,B-y,C-30°
=A+B+C=34°+30°+y°=180°
=64°+y°=180°
y°=180°-64°=116°
so:z+y=180°(Linear pair)
z+116°=180°
=180°-116°=64°. z=64°
=∆BED=z+D+E=180°(angle sum properties of∆)
=64°+45°+E=180°. 180°-109°=71°
E=71°
So,x=
E+x=180°(Linear pair)
x=180°-71°=109°
x=109°
Value of x=109°
- 3