Question

1. solve for x and find each angle. hint= how many degrees does a triangle add up to? 180 degrees set up the equation and solve. x = degrees m<a= degrees m<t= degrees m<c= degrees the outlined content above was added from outside of formative. app.formative.com

Explanation:

Step1: Set up equation

Since the sum of angles in a triangle is 180 degrees, we have $(3x - 17)+(x + 40)+(2x-5)=180$.

Step2: Combine like - terms

Combining the x - terms and the constant terms: $(3x+x + 2x)+(-17 + 40-5)=180$, which simplifies to $6x+18 = 180$.

Step3: Isolate the variable term

Subtract 18 from both sides: $6x=180 - 18$, so $6x=162$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{162}{6}=27$.

Step5: Find angle A

Substitute $x = 27$ into the expression for angle A: $m\angle A=3x-17=3\times27-17=81 - 17=64$ degrees.

Step6: Find angle T

Substitute $x = 27$ into the expression for angle T: $m\angle T=2x - 5=2\times27-5=54 - 5=49$ degrees.

Step7: Find angle C

Substitute $x = 27$ into the expression for angle C: $m\angle C=x + 40=27+40=67$ degrees.

Answer:

$x = 27$ degrees
$m\angle A=64$ degrees
$m\angle T=49$ degrees
$m\angle C=67$ degrees