Question

learning target: apply the angle ad given: m∠abc = 3x + 3 m∠cbd = 6x + 1 m∠abd = 40° find: m∠cbd and m∠abc

Explanation:

Step1: Use angle - addition postulate

Since $\angle ABD=\angle ABC+\angle CBD$, we have the equation $(3x + 3)+(6x + 1)=40$.

Step2: Combine like - terms

Combining like - terms on the left - hand side of the equation gives $9x+4 = 40$.

Step3: Solve for x

Subtract 4 from both sides: $9x=40 - 4=36$. Then divide both sides by 9, so $x = 4$.

Step4: Find $m\angle ABC$

Substitute $x = 4$ into the expression for $m\angle ABC$: $m\angle ABC=3x + 3=3\times4+3=12 + 3=15^{\circ}$.

Step5: Find $m\angle CBD$

Substitute $x = 4$ into the expression for $m\angle CBD$: $m\angle CBD=6x + 1=6\times4+1=24 + 1=25^{\circ}$.

Answer:

$m\angle ABC = 15^{\circ}$, $m\angle CBD=25^{\circ}$