Question

question 5 (3 points) use the diagram to fill in the indicated measurements. (hint: option, k will give you the degree symbol) x = m∠abd = m∠dbc = blank 1: blank 2: blank 3:

Explanation:

Step1: Set up equation

Since $\angle ABD$ and $\angle DBC$ are a linear - pair, their sum is $180^{\circ}$. So, $(4x + 6)+(11x-6)=180$.
Combining like - terms: $4x+11x+6 - 6=180$, which simplifies to $15x=180$.

Step2: Solve for x

Dividing both sides of the equation $15x = 180$ by 15, we get $x=\frac{180}{15}=12$.

Step3: Find $m\angle ABD$

Substitute $x = 12$ into the expression for $\angle ABD$: $m\angle ABD=4x + 6$.
$m\angle ABD=4\times12+6=48 + 6=54^{\circ}$.

Step4: Find $m\angle DBC$

Substitute $x = 12$ into the expression for $\angle DBC$: $m\angle DBC=11x-6$.
$m\angle DBC=11\times12-6=132 - 6=126^{\circ}$.

Answer:

Blank 1: 12
Blank 2: $54^{\circ}$
Blank 3: $126^{\circ}$