Answer:
[tex]\angle CAD = 67.5^{\circ}[/tex]
Step-by-step explanation:
Given :
In the given figure which is not drawn to scale, AB is perpendicular to AD
Measure of [tex]\angle CAD[/tex] is three times measure of [tex]\angle BAC[/tex]
To find : Measure of [tex]\angle CAD[/tex]
Solution :
Let [tex]\angle BAC[/tex] be x .
Therefore, as measure of [tex]\angle CAD[/tex] is three times measure of [tex]\angle BAC[/tex], [tex]\angle CAD=3x[/tex]
Also, as AB is perpendicular to AD, we get
[tex]\angle BAD=90^{\circ}\\\angle BAC+\angle CAD=90^{\circ}\\x+3x=90^{\circ}\\4x=90^{\circ}\\x=\frac{90}{4}=\frac{45}{2}=22.5^{\circ}[/tex]
Therefore, [tex]\angle CAD=3x=3\times 22.5=67.5^{\circ}[/tex]
