Chapter 7.3, Problem 23PSC

To determine

To calculate : The measures of the three remaining angles

Answer to Problem 23PSC

The measures of the three remaining angles is $a={40}^0$ , $b={50}^0$ and $c={130}^0$

Explanation of Solution

Given information : The following information is given

Seven angles of decagon measure up to ${1220}^0$

Exactly two of remaining are complementary

Exactly two of remaining are supplementary

Formula used : The sum of the angles for a polygon with n sides will be equal to

  $s=(n-2){180}^0$

Calculation : We use the formula $s=(n-2){180}^0$ to find out the total sum of the angles. Thus, we get

  $s={1440}^0$

Let the other angles be a, b and c respectively. Thus, we get

  $a+b+c={1440}^0-{1220}^0={220}^0$

  $a+b={90}^0$

  $c+b={180}^0$

Thus, solving the above three equations, we get

  $a={40}^0$ , $b={50}^0$ and $c={130}^0$