Hey ! there
Answer:
- Angle z is equal to <u>1</u><u>1</u><u>4</u><u> </u><u>Degrees </u><u>.</u>
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 <u>z </u><u>.</u>
We are giving numbering to some angles which are important for solving the question So that there's ease in the explanation .
- Angle 1 = <u>(</u><u> </u><u>x </u><u>+</u><u> </u><u>1</u><u>5</u><u> </u><u>)</u><u>°</u>
- Angle 2 = <u>(</u><u> </u><u>3x</u><u> </u><u>-</u><u> </u><u>2</u><u>4</u><u> </u><u>)</u><u>°</u>
- Angle 3 = <u>x</u><u>°</u>
- Angle 4 = <u>z</u><u>°</u>
<u> </u>
<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>
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 ,
Adding 24 on both sides :
Simplifying it ,
Dividing with 4 on both sides :
We get ,
- <u>Therefore</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>x </u><u>is </u><u>5</u><u>1</u><u>°</u><u> </u><u>.</u>
<u>According</u><u> to</u><u> question</u><u> </u><u>,</u><u> </u>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° )
We know that ,
- x = <u>5</u><u>1</u><u>°</u>
So , substituting value of x ,
Simplifying it :
Subtracting 66 from both sides :
On further calculations , We get :
- <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value</u><u> of</u><u> </u><u>angle </u><u>z </u><u>is </u><u>1</u><u>1</u><u>4</u><u>°</u><u> </u><u>.</u>
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<u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>