Question

1. in the figure to the right, the two angles form a linear pair. find m∠abd

m∠abd + m∠dbc = m∠abc

Explanation:

Step1: Recall linear - pair property

Since $\angle ABD$ and $\angle DBC$ form a linear - pair, $\angle ABC = 180^{\circ}$.

Step2: Substitute known values

Let $m\angle ABD=x$ and $m\angle DBC = 130^{\circ}$. Then $x + 130^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle ABD$

Subtract $130^{\circ}$ from both sides of the equation: $x=180^{\circ}-130^{\circ}$.
$x = 50^{\circ}$

Answer:

$m\angle ABD = 50^{\circ}$