Question

PLEASE HELP, REPOSTED QUESTION MULTIPLE TIMES

a. Write an equation to find the value of x.
b. Show how to solve the equation.
c. Find the measure of the smallest interior angle of the triangle.
When answering an extended response question, you can describe how you are going to do the problem and then carry out the steps. For the exercise, begin with the following observation and write a 4-point response.

The largest exterior angle has measure x+8 and the smallest interior angle is a supplement of that angle.

Answer 1

the smallest interior angle is 56,x=116

Explanation:

the interior angle is supplementary, so Each exterior angle has to be less than 180 degrees of its corresponding interior angle, so the interior angles are (180 - x), (180 - (x+4)), and (180 - (x+8)).

Equation:(180 - x) + (180 - (x+4)) + (180 - (x+8)) = 180

Solve:

Simplify both sides of the equation.

180−x+180−(x+4)+180−(x+8)=180

180+−x+180+−x+−4+180+−x+−8=180

(−x+−x+−x)+(180+180+−4+180+−8)=180(Combine Like Terms)

−3x+528=180

−3x+528=180

Step 2: Subtract 528 from both sides.

−3x+528−528=180−528

−3x=−348

Step 3: Divide both sides by -3.

−3x/-3=-348/-3

x=116

since x=116

the largest exterior angle is x+8, and the smallest interior angle is a supplement of that(Supplement: angle >180) we need to add 116 and 8 so

116+8=124 we need to subtract 124 from 180 since the interior angle is a supplement of the exterior angle.

so 180-124=56

the smallest interior angle is 56