Given that the angles $\angle ADC$ and $\angle CBD$ are complementary, their measures add up to 90°. Additionally, $\angle ADC$ is twice the size of $\angle CBD$.

1a. Which equation represents this relationship?

Let:

• $x$ = measure of $\angle CBD$
• Since $\angle ADC$ is twice $\angle CBD$, the measure of $\angle ADC = 2x$.

Since these angles are complementary: $x + 2x = 90$

So the correct equation is:

Answer:
A. $x + 2x = 90$

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1b. What is the measure of $\angle ADC$?

From the equation $x + 2x = 90$, solve for $x$:

$3x = 90 \quad \Rightarrow \quad x = 30^\circ$

Thus, $\angle CBD = 30^\circ$.
Now, $\angle ADC = 2x = 2(30^\circ) = 60^\circ$.

Answer:
C. 60°

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Would you like a further breakdown or more questions?

Here are 5 related questions:

1. What is the definition of supplementary angles?
2. If two angles are complementary and one is three times the other, how would you set up an equation?
3. How do you convert degrees to radians?
4. What is the complement of a 40° angle?
5. Can an angle be both complementary and supplementary?

Tip: Complementary angles always sum to 90°, which is useful for solving many geometry problems.