Question

find m∠iuv if m∠tuv = 13x + 1, m∠tui = 84°, and m∠iuv = 5x + 5.

Explanation:

Step1: Use angle - addition postulate

We know that $m\angle TUV=m\angle TUI + m\angle IUV$. Substituting the given expressions, we get $13x + 1=84+(5x + 5)$.

Step2: Simplify the equation

First, simplify the right - hand side: $13x + 1=84 + 5x+5$, which becomes $13x + 1=5x + 89$.

Step3: Solve for x

Subtract $5x$ from both sides: $13x-5x + 1=5x-5x + 89$, so $8x+1 = 89$. Then subtract 1 from both sides: $8x+1 - 1=89 - 1$, giving $8x=88$. Divide both sides by 8: $x=\frac{88}{8}=11$.

Step4: Find $m\angle IUV$

Substitute $x = 11$ into the expression for $m\angle IUV$. Since $m\angle IUV=5x + 5$, then $m\angle IUV=5\times11 + 5=55 + 5=60$.

Answer:

$60$