Chapter 1.3, Problem 9PSA

To determine

To Find: The measure of the $\angle ABD$ .

Answer to Problem 9PSA

  $\angle ABD=135°$

Explanation of Solution

Given:

  $\angle ABD=\left(3x\right)°,\angle DBC=x°$

  

Concept Used:

Sum of linear pair of angle is $180°$

Calculation:

Since, the sum of linear pair of angle is $180°$

  $\begin{array}{l}\angle ABD+\angle DBC=180°\\ \Rightarrow \left(3x\right)°+\left(x\right)°=180°\\ \Rightarrow \left(4x\right)°=180°\\ \Rightarrow x=45°\\ \Rightarrow \angle ABD=\left(3\times 45\right)°=135°\\ \therefore \angle ABD=135°\end{array}$

Conclusion:

  $\angle ABD=135°$