Question

8 fill in the blank 1 point point d is in the interior of ∠abc, m∠abc = 10x - 7, m∠abd = 6x + 5, and m∠dbc = 36°. what is m∠abd? m∠abd = type your answer... 9 multiple choice 1 point p lies in the interior of ∠rst. m∠rsp = 40° and m∠tsp = 10°. m∠rst = _?

Explanation:

Step1: Use angle - addition postulate

Since point D is in the interior of $\angle ABC$, we know that $m\angle ABC=m\angle ABD + m\angle DBC$. So, $10x - 7=(6x + 5)+36$.

Step2: Solve the equation for x

First, simplify the right - hand side of the equation: $10x - 7=6x+41$. Then, subtract $6x$ from both sides: $10x-6x - 7=6x - 6x+41$, which gives $4x-7 = 41$. Next, add 7 to both sides: $4x-7 + 7=41 + 7$, so $4x=48$. Divide both sides by 4: $x = 12$.

Step3: Find $m\angle ABD$

Substitute $x = 12$ into the expression for $m\angle ABD$. $m\angle ABD=6x + 5$. So, $m\angle ABD=6\times12 + 5=72 + 5=77^{\circ}$.

Answer:

$77^{\circ}$