Q:

PLEASE HELP, REPOSTED QUESTION MULTIPLE TIMESa. 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.

Accepted Solution

A:
Answer:the smallest interior angle is 56,x=116Step-by-step explanation:the interior Β 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. 180βˆ’x+180βˆ’(x+4)+180βˆ’(x+8)=180 180+βˆ’x+180+βˆ’x+βˆ’4+180+βˆ’x+βˆ’8=180 (βˆ’x+βˆ’x+βˆ’x)+(180+180+βˆ’4+180+βˆ’8)=180(Combine Like Terms) βˆ’3x+528=180 βˆ’3x+528=180 Step 2: Subtract 528 from both sides. βˆ’3x+528βˆ’528=180βˆ’528 βˆ’3x=βˆ’348 Step 3: Divide both sides by -3. βˆ’3x/-3=-348/-3 Β x=116since x=116the largest exterior angle Β 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 Β we need to subtract 124 from 180 since the interior angle is a supplement of the exterior angle.so 180-124=56the smallest interior angle is 56