Question

g. find m∠abd.
h. find m∠dbc.
i. find m∠xyw.
j. find m∠wyz.

Explanation:

Step1: Note that $\angle XYW$ and $\angle WYZ$ are complementary (since $\angle XYZ = 90^{\circ}$).

So, $(1\frac{1}{4}x - 10)+(\frac{3}{4}x + 20)=90$.

Step2: Combine like - terms.

$(\frac{5}{4}x-10)+(\frac{3}{4}x + 20)=90$.
$\frac{5}{4}x+\frac{3}{4}x-10 + 20=90$.
$\frac{5x + 3x}{4}+10=90$.
$\frac{8x}{4}+10=90$.
$2x+10 = 90$.

Step3: Solve for $x$.

Subtract 10 from both sides: $2x=90 - 10$.
$2x=80$.
Divide both sides by 2: $x = 40$.

Step4: Find $m\angle XYW$.

Substitute $x = 40$ into the expression for $m\angle XYW$: $m\angle XYW=1\frac{1}{4}x-10$.
$m\angle XYW=\frac{5}{4}\times40-10$.
$m\angle XYW = 50-10$.
$m\angle XYW = 40^{\circ}$.

Step5: Find $m\angle WYZ$.

Substitute $x = 40$ into the expression for $m\angle WYZ$: $m\angle WYZ=\frac{3}{4}x + 20$.
$m\angle WYZ=\frac{3}{4}\times40+20$.
$m\angle WYZ=30 + 20$.
$m\angle WYZ = 50^{\circ}$.

Answer:

I. $m\angle XYW = 40^{\circ}$
J. $m\angle WYZ = 50^{\circ}$