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6. In the diagram below, which is not drawn to scale, AB is perpendicular to AD. If the measure of ZCAD
is three times the measure of ZBAC, determine the measure of LCAD.

6 In the diagram below which is not drawn to scale AB is perpendicular to AD If the measure of ZCAD is three times the measure of ZBAC determine the measure of class=

Respuesta :

cookie928
4x = 90
X = 22.5
The answer the the problem is 3x, so 67.5 :) have a great day

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]

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