Question

1. (mangle efg = 119). find (mangle efh) and (mangle gfh). (overrightarrow{bd}) bisects (angle abc). find (mangle abd), (mangle cbd), and (mangle abc). 31. a (6x + 14)° d (3x + 29)° b c

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD=m\angle CBD$. So we set up the equation $6x + 14=3x+29$.
$6x+14 = 3x + 29$
$6x-3x=29 - 14$
$3x=15$
$x = 5$

Step2: Find $m\angle ABD$

Substitute $x = 5$ into the expression for $m\angle ABD=(6x + 14)^{\circ}$.
$m\angle ABD=6\times5+14=30 + 14=44^{\circ}$

Step3: Find $m\angle CBD$

Since $m\angle CBD=m\angle ABD$, then $m\angle CBD = 44^{\circ}$

Step4: Find $m\angle ABC$

$m\angle ABC=m\angle ABD+m\angle CBD$
$m\angle ABC=44^{\circ}+44^{\circ}=88^{\circ}$

Answer:

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