Answer:
[tex]m\angle CAB=65^\circ[/tex]
Step-by-step explanation:
Angles and Lines
It's convenient to recall two basic principles of angles:
The sum of internal angles in a triangle is 180°
Two linear angles are supplementary, i.e. they sum 180°.
Angles ABC and CBD are linear. Since we know the measure of angle CBD, thus the measure of angle ABC is 180°-6x.
Now focus on the triangle. The sum of its internal angles is:
x + 40 + 3x + 10 + 180 - 6x = 180
Simplifying:
-2x + 230 = 180
Subtracting 230:
-2x = -50
Dividing by -2:
x = -50 / (-2) = 25
x = 25°
Now find the measure of angle CAB
[tex]m\angle CAB=x+40=25+40=65[/tex]
[tex]\mathbf{m\angle CAB=65^\circ}[/tex]
