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Answer:
- Angle z is equal to 114 Degrees .
Step-by-step explanation:
In this question we're given with four interior and four exterior angles of quadrilateral . And we're asked to find the value of angle z .
We are giving numbering to some angles which are important for solving the question So that there's ease in the explanation .
Solution : -
For finding value of angle z , we need to find the value of angle x . So
This is because they are Linear angles and sum of linear angles is equal to 180°.
Now ,
[tex] \dashrightarrow \qquad \: 3x - 24 + x = 180[/tex]
Adding 24 on both sides :
[tex]\dashrightarrow \qquad \:3x - \cancel{ 24} + \cancel{24 } + x = 180 + 24[/tex]
Simplifying it ,
[tex]\dashrightarrow \qquad \:4x = 204[/tex]
Dividing with 4 on both sides :
[tex]\dashrightarrow \qquad \: \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{204}{4} }[/tex]
We get ,
[tex]\dashrightarrow \qquad \: \underline{\boxed{\frak{x = 51^{\circ}}}}[/tex]
- Therefore , value of x is 51° .
According to question , we need to find the value of angle z . So ,
- Angle 1 + Angle 4 = 180° ( They are Linear angles , Therefore there sum is equal to 180° )
[tex] \dashrightarrow \qquad \:( x + 15) + z = 180[/tex]
We know that ,
So , substituting value of x ,
[tex] \dashrightarrow \qquad \: (51+ 15) + z = 180[/tex]
Simplifying it :
[tex] \dashrightarrow \qquad \: 66 + z = 180[/tex]
Subtracting 66 from both sides :
[tex] \dashrightarrow \qquad \: \cancel{ 66 }+ z - \cancel{66}= 180 - 66[/tex]
On further calculations , We get :
[tex] \dashrightarrow \qquad \: \pink{\underline{\boxed{\frak{z = 114^{\circ} }}}} \quad\bigstar[/tex]
- Henceforth , value of angle z is 114° .
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