Question

1. if $mangle dbc = 74^{circ}$ and $mangle abc = 119^{circ}$, find $mangle abd$.

Explanation:

Step1: Identify angle - relationship

We know that $\angle ABC=\angle ABD+\angle DBC$.

Step2: Solve for $\angle ABD$

We can rewrite the equation as $\angle ABD=\angle ABC - \angle DBC$. Given that $m\angle ABC = 119^{\circ}$ and $m\angle DBC=74^{\circ}$, we substitute the values: $\angle ABD=119^{\circ}-74^{\circ}$.

Step3: Calculate the result

$119 - 74=45$, so $m\angle ABD = 45^{\circ}$.

Answer:

$45^{\circ}$