Question

question 12 (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: Note angle - sum property

Since $\angle ABC = 90^{\circ}$ and $\angle ABD=2x^{\circ}$, $\angle DBC = 3x^{\circ}$, and $\angle ABD+\angle DBC=\angle ABC$, we have the equation $2x + 3x=90$.

Step2: Solve the equation for $x$

Combining like - terms in $2x + 3x=90$, we get $5x = 90$. Then, dividing both sides by 5, we have $x=\frac{90}{5}=18$.

Step3: Find $\angle ABD$

Substitute $x = 18$ into the expression for $\angle ABD$. So, $m\angle ABD=2x=2\times18 = 36^{\circ}$.

Step4: Find $\angle DBC$

Substitute $x = 18$ into the expression for $\angle DBC$. So, $m\angle DBC=3x=3\times18 = 54^{\circ}$.

Answer:

Blank 1: 18
Blank 2: $36^{\circ}$
Blank 3: $54^{\circ}$