1) Given this pentagon, let's find each measure of the angle x, y, and z we can notice that there are several supplementary angles.
2) Since we have a linear pair (∠80º and ∠y), then we can write:
m∠y = 180º -80º
m∠y = 100º
m∠x Another linear pair with ∠95º:
m∠x= 180º -95º
m∠x =85º
Let's visualize all the angles within that Pentagon:
Since there is a pentagon, then we can find the Sum of its interior angles by
S = 180(n-2)
S = 180( 5-2)
S =180(3)
S= 540º
And we can find the angle z by subtracting from 540º the sum of the other angles:
Hence m∠z = 540º -(95+127+100+118)
m∠z = 540º -(95+127+100+118)
m∠z = 100º
3) So the measures of angles x, y, and z are:
m∠x =85º, m∠y = 100º and m∠z = 100º