Consider the line segment UZ with a point W between U and Z. If UW = 6x - 15, WZ = 2x + 5, and the entire...
2. If m∠RST = 136° and m∠RSU = 92°, find m∠TSU.
3. Solve for x.
To find the value of x, we set up the equation based on the given segment lengths: UW + WZ = UZ. So, (6x - 15) + (2x + 5) = 70. Simplifying, we get 8x - 10 = 70. Adding 10 to both sides gives 8x = 80. Dividing by 8, we find x = 10.
To find m∠TSU, we use the fact that m∠RST = m∠RSU + m∠TSU. So, 136° = 92° + m∠TSU. Subtracting 92° from both sides gives m∠TSU = 44°.
To solve for x, we use the equation formed by the angles around a point: 35° + (2x + 16)° + (4x + 3)° = 360°. Simplifying, we get 35 + 2x + 16 + 4x + 3 = 360. Combining like terms, we have 6x + 54 = 360. Subtracting 54 from both sides gives 6x = 306. Dividing by 6, we find x = 51.
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