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Sagot :

TheAmethyst

Hey ! there

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 .

  • Angle 1 = ( x + 15 )°

  • Angle 2 = ( 3x - 24 )°

  • Angle 3 = x°

  • Angle 4 = z°

Solution : -

For finding value of angle z , we need to find the value of angle x . So

  • Angle 2 + Angle 3 = 180°

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 ,

  • x = 51°

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° .

#Keep Learning

semsee45

Answer:

114 Degrees

Step-by-step explanation:

Theorem:  Angles on a straight line add up to 180°

Using this theorem, find x:

⇒ x + (3x - 24) = 180°

⇒ 4x - 24 = 180°

⇒ 4x = 204°

⇒ x = 51°

Using the found value of x and the straight line theorem to find z:

⇒ (x + 15) + z = 180°

⇒ (51 + 15) + z = 180°

⇒ 66 + z = 180°

⇒ z = 180° - 66

⇒ z = 114°

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