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Find the value of each variable.
A four-sided polygon has angles labeled as follows: y degrees, 102 degrees, 81 degrees, z degrees. A straight line containing the angle labeled z degrees forms a second angle, labeled 115 degrees.
y=
z=

Find the value of each variable A foursided polygon has angles labeled as follows y degrees 102 degrees 81 degrees z degrees A straight line containing the angl class=

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Answer:

[tex]y=112\degree[/tex]

[tex]z=65\degree[/tex]

Step-by-step explanation:

The sum of adjacent angles on a straight line is [tex]180\degree[/tex].

[tex]\Rightarrow 115\degree+z\degree=180\degree[/tex]

[tex]\Rightarrow z\degree=180\degree-115\degree[/tex]

[tex]\Rightarrow z\degree=65\degree[/tex]

The sum of angles in a quadrilateral is 360 degrees.

[tex]\Rightarrow 65\degree+81\degree +102\degree +y=360\degree[/tex]

[tex]\Rightarrow 248\degree +y=360\degree[/tex]

[tex]\Rightarrow y=360\degree-248\degree[/tex]

[tex]\Rightarrow y=112\degree[/tex]

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