Question

1. if m∠dba = 3x + 12 and m∠dbc = 5x - 2, find x, m∠dba & m∠dbc.

x=
m∠dba=
m∠dbc=

Explanation:

Step1: Assume angles are complementary

Since $\angle DBA$ and $\angle DBC$ are adjacent angles in a rectangle and $\angle ABC = 90^{\circ}$, we have $m\angle DBA+m\angle DBC = 90^{\circ}$. So, $(3x + 12)+(5x-2)=90$.

Step2: Simplify the left - hand side

Combine like terms: $3x+5x+12 - 2=90$, which gives $8x + 10=90$.

Step3: Solve for x

Subtract 10 from both sides: $8x=90 - 10=80$. Then divide both sides by 8: $x=\frac{80}{8}=10$.

Step4: Find $m\angle DBA$

Substitute $x = 10$ into the expression for $m\angle DBA$: $m\angle DBA=3x+12=3\times10 + 12=30+12=42^{\circ}$.

Step5: Find $m\angle DBC$

Substitute $x = 10$ into the expression for $m\angle DBC$: $m\angle DBC=5x-2=5\times10-2=50 - 2=48^{\circ}$.

Answer:

$x = 10$
$m\angle DBA=42^{\circ}$
$m\angle DBC=48^{\circ}$