Chapter 1.3, Problem 6PSA

To determine

To find: How large is $m\angle ABD$ .

Answer to Problem 6PSA

  $m\angle ABD=54°$

Explanation of Solution

Given:

  

Measures of angle ABD and DBC are in the ratio 3: 2.

Concept Used:

Angles formed at point B are complementary angle.

Calculation:

Since, measures of angle ABD and DBC are in the ratio 3: 2.

  

Since, angles formed at the corner are complementary angle.

  $\begin{array}{l}\Rightarrow \angle ABC=\angle ABD+\angle DBC\\ \Rightarrow 90°=3x+2x\\ \Rightarrow 90°=5x\\ \Rightarrow x=18°\\ \Rightarrow \angle ABD=3\times 18°=54°\end{array}$

Conclusion:

  $\angle ABD=54°$