Question

I have been stuck for about 20 minutes. looking for help.

Answer 1

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,

`\begin{gathered} 15x-2+7x+4=90^0 \\ 22x+2=90^0 \\ 22x=90-2 \\ 22x=88 \\ x=(88)/(22) \\ x=4 \end{gathered}`

Substitute the value of x in each angle.

The measure of angle BAC is,

`\begin{gathered} \angle BAC=(15x-2)^0 \\ =15(4)^0-2^0 \\ =60^0-2^0 \\ =58^0 \end{gathered}`

The measure of angle DAC is,

`\begin{gathered} \angle DAC=(7x+4)^0 \\ =7(4)^0+4^0 \\ =28^0+4^0 \\ =32^0 \end{gathered}`

Hence, measure of anlge BAC is 58 degree and the measure of angle CAD is 32 degree.