Question

Examine the following diagram:میراA8x + 1D6x + 5What is the measure of ZDBC?0 20 6°0 41°0 49°

Answer 1

Given:

• Measure of ∠ABC = 90 degrees

,

• Measure of ∠ABD = 8x + 1

,

• Measure of ∠DBC = 6x + 5

Let's find the measure of ∠DBC.

Since ∠ABC is a right angle, it measures 90 degrees.

Thus, we have:

m∠ABD + m∠DBC = 90

Now, we have the equation:

$8x+1+6x+5=90$

Let's solve for x in the equation:

Combine like terms.

$\begin{gathered} 8x+6x+1+5=90 \\ \\ 14x+6=90 \end{gathered}$

Subtract 6 from both sides:

$\begin{gathered} 14x+6-6=90-6 \\ \\ 14x=84 \end{gathered}$

Divide both sides by 14:

$\begin{gathered} \frac{14x}{14}=\frac{84}{14} \\ \\ x=6 \end{gathered}$

Now, to find the measure of ∠DBC, substitute 6 for x in (6x + 5):

m∠DBC = 6(6) + 5

m∠DBC = 36 + 5

m∠DBC = 41 degrees.

• ANSWER:

41°