Chapter 7.4, Problem 17PSC

To determine

Explanation of a regular semi octagon is to be given, and values of x and y are to be found

Answer to Problem 17PSC

values of x and y are $y=18$ and $x=27$

Explanation of Solution

Given information : A semi octagon ABCDE is given

A semi octagon is half of a regular octagon, that divides the angles of the opposite vertices into two equal halves.

Thus, we know that the values of angles E and A are

  $m\angle E=3x+3y+9={135}^0$

  $m\angle A=2x+y-4\frac{1}{2}=\frac{{135}^0}{2}$

Hence, on solving the above two equations, we get

  $y=18$ and $x=27$