Question

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

Explanation:

Step1: Recall linear - pair property

Since $\angle ABD$ and $\angle DBC$ form a linear pair, $m\angle ABD + m\angle DBC=180^{\circ}$ (a linear - pair of angles is supplementary). So, $(5x + 10)+(2x-5)=180$.

Step2: Combine like terms

Combine the $x$ terms and the constant terms on the left - hand side: $(5x+2x)+(10 - 5)=180$, which simplifies to $7x + 5=180$.

Step3: Solve for $x$

Subtract 5 from both sides: $7x=180 - 5=175$. Then divide both sides by 7: $x=\frac{175}{7}=25$.

Step4: Find $m\angle DBC$

Substitute $x = 25$ into the expression for $m\angle DBC$ which is $2x-5$. So, $m\angle DBC=2\times25-5=50 - 5=45^{\circ}$.

Answer:

$45^{\circ}$