Question

1. find the m∠abd if m∠abc=(19y + 25)°. (14y + 6)° (8y + 5)°

Explanation:

Step1: Use angle - addition postulate

Since $\angle ABC=\angle ABD+\angle DBC$, we have $(19y + 11)=(14y + 6)+(8y+5)$.

Step2: Simplify the right - hand side of the equation

$(14y + 6)+(8y+5)=14y+8y + 6 + 5=22y+11$.
So, the equation becomes $19y + 11=22y+11$.

Step3: Solve for y

Subtract $19y$ from both sides: $19y+11-19y=22y + 11-19y$, which gives $11 = 3y+11$.
Then subtract 11 from both sides: $11-11=3y+11 - 11$, resulting in $0 = 3y$.
Divide both sides by 3: $y = 0$.

Step4: Find the measure of $\angle ABD$

Substitute $y = 0$ into the expression for $\angle ABD$.
$\angle ABD=(14y + 6)^{\circ}$.
When $y = 0$, $\angle ABD=(14\times0 + 6)^{\circ}=6^{\circ}$.

Answer:

$6^{\circ}$