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

List The Angles Of The Given Triangle From Smallest To Largest Explain Your Reasoning Solve For X class=

Sagot :

annie413

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

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