Given:
Angle BAC is 15x-2 degree.
Angle DAC is 7x+4 degree.
The objective is to find the measure of each angle.
Since the given triangle is a right angled triangle.
So the sum of the angles in a right angle is a complementary angle 90 degree.
Then, the value of x can be calculated as,
[tex]\begin{gathered} 15x-2+7x+4=90^0 \\ 22x+2=90^0 \\ 22x=90-2 \\ 22x=88 \\ x=\frac{88}{22} \\ x=4 \end{gathered}[/tex]
Substitute the value of x in each angle.
The measure of angle BAC is,
[tex]\begin{gathered} \angle BAC=(15x-2)^0 \\ =15(4)^0-2^0 \\ =60^0-2^0 \\ =58^0 \end{gathered}[/tex]
The measure of angle DAC is,
[tex]\begin{gathered} \angle DAC=(7x+4)^0 \\ =7(4)^0+4^0 \\ =28^0+4^0 \\ =32^0 \end{gathered}[/tex]
Hence, measure of anlge BAC is 58 degree and the measure of angle CAD is 32 degree.
