Question

if ∠abc = 155, what are m∠abd and m∠cbd? a (4x - 20)° d (3x + 14)° b c

Explanation:

Step1: Set up equation from angle - sum property

Since $\angle ABC=\angle ABD+\angle CBD$, we have $(4x - 20)+(3x + 14)=155$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $4x+3x-20 + 14=155$, which simplifies to $7x-6 = 155$.

Step3: Solve for $x$

Add 6 to both sides of the equation: $7x-6 + 6=155 + 6$, so $7x=161$. Then divide both sides by 7: $x=\frac{161}{7}=23$.

Step4: Find $\angle ABD$

Substitute $x = 23$ into the expression for $\angle ABD$: $\angle ABD=4x-20=4\times23-20=92 - 20=72^{\circ}$.

Step5: Find $\angle CBD$

Substitute $x = 23$ into the expression for $\angle CBD$: $\angle CBD=3x + 14=3\times23+14=69 + 14=83^{\circ}$.

Answer:

$m\angle ABD = 72^{\circ}$, $m\angle CBD=83^{\circ}$