Chapter 2.2, Problem 20PSB

To determine

To calculate: $\angle DBC$

Answer to Problem 20PSB

  $-{10}^{\circ }$ (Question is incomplete)

Explanation of Solution

Given information: $XY\perp YW,AB\perp BC$

  

Calculation:

  $\begin{array}{l}XY\perp YW\&AB\perp BC\\ \Rightarrow \angle XYW={90}^{\circ }\&2x+y-50={90}^{\circ }\\ \Rightarrow x+y={90}^{\circ }\&2x+y-50={90}^{\circ }\\ \therefore x+y={90}^{\circ }\mathrm{....}(1)\&2x+y={140}^{\circ }\mathrm{....}(2)\end{array}$

Solving equation (1) and (2)

  $x={50}^{\circ }$ And $y={40}^{\circ }$

  $\begin{array}{}$ \therefore \angle DBC={(Y-50)}^{\circ }$$ ={(-10)}^{\circ }$\end{array}$