Question

point d is in the interior of $angle abc$, $mangle abc = 10x - 7$, $mangle abd = 6x + 5$, and $mangle dbc = 36^{circ}$. what is $mangle abd$? $mangle abd=$ type your answer...

Explanation:

Step1: Use angle - addition postulate

Since $\angle ABC=\angle ABD+\angle DBC$, we have the equation $10x - 7=(6x + 5)+36$.

Step2: Simplify the right - hand side of the equation

$(6x + 5)+36=6x+41$, so the equation becomes $10x - 7=6x + 41$.

Step3: Solve for x

Subtract $6x$ from both sides: $10x-6x - 7=6x-6x + 41$, which simplifies to $4x-7 = 41$. Then add 7 to both sides: $4x-7 + 7=41 + 7$, getting $4x=48$. Divide both sides by 4: $x = 12$.

Step4: Find $m\angle ABD$

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

Answer:

$77$