Question

question 2 (1 point) using the following diagram, find m∠abc and m∠cbd. m∠abc = m∠cbd = blank 1: blank 2:

Explanation:

Step1: Set up an equation

Since $\angle ABC$ and $\angle CBD$ are complementary (as $\angle ABE = 90^{\circ}$), we have $(11x - 2)+(5x - 4)=90$.

Step2: Simplify the left - hand side

Combine like terms: $11x+5x-2 - 4=90$, which gives $16x-6 = 90$.

Step3: Solve for $x$

Add 6 to both sides: $16x=90 + 6=96$. Then divide both sides by 16, so $x=\frac{96}{16}=6$.

Step4: Find $m\angle ABC$

Substitute $x = 6$ into the expression for $\angle ABC$: $m\angle ABC=11x-2=11\times6-2=66 - 2=64^{\circ}$.

Step5: Find $m\angle CBD$

Substitute $x = 6$ into the expression for $\angle CBD$: $m\angle CBD=5x-4=5\times6-4=30 - 4=26^{\circ}$.

Answer:

Blank 1: $64^{\circ}$
Blank 2: $26^{\circ}$