Question

List the angles of the given triangle from smallest to largest. Explain your reasoning. Solve for x.

Answer 1

Answer:

Smallest to Largest: Angle ACD, Angle ADC, Angle CAD, Angle ACB

Step-by-step explanation:

To find the angles, let's first solve for x.

Let's call the missing side angle ACD= y

We know that there are 180 degrees in a triangle. So we can write the equation,

6x+4+(4x-2)+y= 180

and, We know that angle ACB is a linear pair with angle ACD, so both angles would add up to 180 degrees. We can write the equation,

9x+16+y=180

Let's now solve for x with both of these equations using elimination.

Simplify the equations,

6x+4+(4x-2)+y= 180 -> 10x+y=178

9x+16+y=180 -> 9x+y=164

-1(10x+y=178) -> -10x-y=-178

-10x-y=-178

9x+y=164

-x= -14

x= 14

Now that we have solved for x, we can find the missing angles.

Angle ACB= 9x+16 -> 9(14)+16= 142 degrees

Angle CAD= 6x+4 -> 6(14)+4= 88 degrees

Angle ADC= 4x-2 -> 4(14)-2= 54 degrees

Angle ACD= 180-(Angle CAD+ Angle ADC) -> 180-(88+54)= 38 degrees