Questions: Solve for x.

Transcript text: Solve for $x$.

Solution

Solution Steps

Step 1: Set up the equation

In triangle TUS, segment CB is parallel to segment US. According to the Triangle Midsegment Theorem, CB = US/2, if C and B are midpoints of TU and TS, respectively. Since UC=CT and SB=BT, C and B are midpoints. Therefore, we have x + 19 = (x + 28)/2

Step 2: Solve the equation

Multiplying both sides of the equation by 2 gives 2(x+19) = x+28. Expanding the left side gives 2x + 38 = x + 28. Subtracting x from both sides gives x + 38 = 28. Finally, subtracting 38 from both sides gives x = -10.

Step 3: Solve for the angles

The sum of angles in a triangle is 180°. Therefore, 49 + 87 + x + 48 = 180. Combining like terms gives 184 + x = 180. Subtracting 184 from both sides gives x = -4.

Final Answer:

x = -10
x = -4

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