Question

$\overline{bd}$ bisects $\angle abc$. find $m\angle abd$, $m\angle cbd$, and $m\angle abc$.
37)
there is an image of angle abc with vertex at b, ba going up, bc going right, and bd as a bisector. the angle between ba and bd is $(6x + 14)°$, and the angle between bd and bc is $(3x + 29)°$

Explanation:

Step1: Set angles equal (bisector property)

$6x + 14 = 3x + 29$

Step2: Solve for x

$6x - 3x = 29 - 14$
$3x = 15$
$x = \frac{15}{3} = 5$

Step3: Calculate $m\angle ABD$

Substitute $x=5$: $6(5) + 14 = 30 + 14 = 44$

Step4: Calculate $m\angle CBD$

Substitute $x=5$: $3(5) + 29 = 15 + 29 = 44$

Step5: Calculate $m\angle ABC$

Sum the two angles: $44 + 44 = 88$

Answer:

$m\angle ABD = 44^\circ$, $m\angle CBD = 44^\circ$, $m\angle ABC = 88^\circ$