Question

1. find m∠stu if m∠itu = 11x - 2, m∠stu = 18x + 1, and m∠sti = 52°.

Explanation:

Step1: Set up the angle - relationship equation

We know that \(m\angle STU=m\angle ITU + m\angle STI\). Substituting the given expressions, we get \(18x + 1=(11x - 2)+52\).

Step2: Simplify the right - hand side of the equation

\((11x - 2)+52=11x+50\). So the equation becomes \(18x + 1=11x + 50\).

Step3: Solve for \(x\)

Subtract \(11x\) from both sides: \(18x-11x + 1=11x-11x + 50\), which simplifies to \(7x+1 = 50\). Then subtract 1 from both sides: \(7x+1 - 1=50 - 1\), so \(7x=49\). Divide both sides by 7: \(x=\frac{49}{7}=7\).

Step4: Find \(m\angle STU\)

Substitute \(x = 7\) into the expression for \(m\angle STU\). \(m\angle STU=18x + 1\). So \(m\angle STU=18\times7+1=126 + 1=127^{\circ}\).

Answer:

\(127^{\circ}\)