Find X in the Angle Equation: (40+X)° and (120+X)° in Triangle Geometry

Question

Calculate X.

00:00 Calculate X

00:04 The adjacent angles form a straight angle (sum to 180)

00:07 Sum and equate to 180, solve for X

00:14 Collect like terms

00:22 Isolate X

00:42 And this is the solution to the problem

To solve for $X$ , we must analyze the configuration formed by the angles $40 + X$ and $120 + X$ .

Step 1: Assume the angles are complementary based on the configuration, meaning they sum to 180 degrees.
Step 2: Formulate the equation based on this assumption: $(40 + X) + (120 + X) = 180$ .
Step 3: Simplify the equation: $40 + X + 120 + X = 180$ .
Step 4: Combine like terms to get $160 + 2X = 180$ .
Step 5: Solve for $X$ by subtracting 160 from both sides to yield $2X = 20$ .
Step 6: Divide by 2 to solve for $X$ , giving $X = 10$ .

Therefore, the value of $X$ is 10.