Question

1. ∠u and ∠w are vertical angles. if m∠u=(6x + 11)° and m∠w=(10x - 9)°, find m∠u.

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set $m\angle U=m\angle W$. So, $6x + 11=10x-9$.

Step2: Solve for x

Subtract $6x$ from both sides: $11 = 10x-6x - 9$, which simplifies to $11=4x - 9$. Then add 9 to both sides: $11 + 9=4x$, so $20 = 4x$. Divide both sides by 4, we get $x = 5$.

Step3: Find $m\angle U$

Substitute $x = 5$ into the expression for $m\angle U$. $m\angle U=6x + 11=6\times5+11=30 + 11=41^{\circ}$.

Answer:

$41^{\circ}$