Question

problem 22: (first taught in lesson 16) ∠a and ∠d are supplementary. if m∠a = 9y - 19 and m∠d = 3y - 5, find m∠a. after you enter your answer press go. m∠a =

Explanation:

Step1: Use supplementary - angle property

Since $\angle A$ and $\angle D$ are supplementary, $m\angle A + m\angle D=180^{\circ}$. So, $(9y - 19)+(3y - 5)=180$.

Step2: Simplify the left - hand side

Combine like terms: $9y+3y-19 - 5 = 180$, which gives $12y-24 = 180$.

Step3: Solve for $y$

Add 24 to both sides: $12y=180 + 24=204$. Then divide both sides by 12: $y=\frac{204}{12}=17$.

Step4: Find $m\angle A$

Substitute $y = 17$ into the expression for $m\angle A$: $m\angle A=9y-19=9\times17-19=153 - 19=122$.

Answer:

$122$