Chapter 1, Problem 34RP

To determine

To calculate: The value of x and y

Answer to Problem 34RP

The values of x and y are $x={10}^o$ and $y={7.5}^o$

Explanation of Solution

Given information: BD is the angle bisector

  $m\angle ABC=25$

Formula used: $\angle ABD=\angle DBC$ (angle bisector)

Calculation: Using the above formula, we put the values of angles $\angle ABD$ and $\angle DBC$ given in the question

Thus, we get

  $\angle ABD={(2x-y)}^o={12.5}^o$

  $\angle DBC={(3y-x)}^o={12.5}^o$

Solving the above two equations for x and y, we get :

  $x={10}^o$

  $y={7.5}^o$