Question

question 8 (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, $(10x + 1)+(9x-11)=180$.

Step2: Simplify the left - hand side

Combine like terms: $10x+9x + 1-11=180$, which gives $19x-10 = 180$.

Step3: Solve for x

Add 10 to both sides: $19x=180 + 10=190$. Then divide both sides by 19, so $x = 10$.

Step4: Find $m\angle ABD$

Substitute $x = 10$ into the expression for $\angle ABD$: $m\angle ABD=10x + 1=10\times10 + 1=101^{\circ}$.

Step5: Find $m\angle DBC$

Substitute $x = 10$ into the expression for $\angle DBC$: $m\angle DBC=9x-11=9\times10-11 = 79^{\circ}$.

Answer:

Blank 1: 10
Blank 2: $101^{\circ}$
Blank 3: $79^{\circ}$