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.
180βx+180β(x+4)+180β(x+8)=180
180+βx+180+βx+β4+180+βx+β8=180
(βx+βx+βx)+(180+180+β4+180+β8)=180(Combine Like Terms)
β3x+528=180
β3x+528=180
Step 2: Subtract 528 from both sides.
β3x+528β528=180β528
β3x=β348
Step 3: Divide both sides by -3.
β3x/-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