Question

find m∠abd and m∠cbd given m∠abc = 77°. (3x + 22)° (5x - 17)° a d b c m∠abd = □° and m∠cbd = □°. 7 8 9 + x y x² √ 4 5 6 × x/x x x¹ x

Explanation:

Step1: Set up equation

Since $\angle ABC=\angle ABD+\angle CBD$, we have $(3x + 22)+(5x-17)=77$.

Step2: Simplify the left - hand side

Combine like terms: $3x+5x+22 - 17=8x + 5$. So, $8x+5 = 77$.

Step3: Solve for x

Subtract 5 from both sides: $8x=77 - 5=72$. Then divide both sides by 8, $x=\frac{72}{8}=9$.

Step4: Find $m\angle ABD$

Substitute $x = 9$ into the expression for $\angle ABD$: $m\angle ABD=3x+22=3\times9 + 22=27+22=49$.

Step5: Find $m\angle CBD$

Substitute $x = 9$ into the expression for $\angle CBD$: $m\angle CBD=5x-17=5\times9-17=45 - 17=28$.

Answer:

$m\angle ABD = 49^{\circ}$ and $m\angle CBD=28^{\circ}$