Chapter 7.1, Problem 12PSB

To determine

The sum of the values of $\angle D$ and $\angle F$ is to be calculated.

Answer to Problem 12PSB

The sum of the values of $\angle D+\angle F={100}^0$

Explanation of Solution

Given information : The following information has been given

  $\angle D+\angle E={110}^0$

  $\angle E+\angle F={150}^0$

Formula used : The sum of angles of a tringle add up to ${180}^0$

Calculation : We know that the sum of angles of a tringle add up to ${180}^0$ . Thus, we can say that

  $\angle D+\angle E={110}^0={180}^0-\angle F\to \angle F={70}^0$

  $\angle E+\angle F={150}^0={180}^0-\angle D\to \angle D={30}^0$

Thus, from the above two equations we can say that

  $\angle D+\angle F={100}^0$