Question

question 4

1. what is the measure of angle bdc?

your answer

Explanation:

Step1: Note angle - sum property

The two angles $(2x)^{\circ}$ and $(4x - 6)^{\circ}$ are complementary, so their sum is $90^{\circ}$. We set up the equation $2x+(4x - 6)=90$.

Step2: Simplify the left - hand side

Combine like terms: $2x+4x-6 = 6x-6$. So the equation becomes $6x - 6=90$.

Step3: Add 6 to both sides

$6x-6 + 6=90 + 6$, which simplifies to $6x=96$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{96}{6}=16$.

Step5: Find the measure of $\angle BDC$

We want to find the measure of $\angle BDC=(4x - 6)^{\circ}$. Substitute $x = 16$ into the expression: $4\times16-6=64 - 6=58^{\circ}$.

Answer:

$58^{\circ}$