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Let's analyze and solve the question:

### Problem Analysis

Given:
1. Angles \( \angle ADC \) and \( \angle CBD \) are complementary, meaning their measures add up to \( 90^\circ \).
2. \( \angle ADC \) is twice the size of \( \angle CBD \).

### Step-by-Step Solution

Let:
- \( x \) be the measure of \( \angle ADC \).
- \( y \) be the measure of \( \angle CBD \).

According to the conditions:
1. \( x + y = 90 \) (since they are complementary).
2. \( x = 2y \) (since \( \angle ADC \) is twice \( \angle CBD \)).

#### Substitute \( x = 2y \) into \( x + y = 90 \):
\[
2y + y = 90
\]
\[
3y = 90
\]
\[
y = 30
\]

Now, substitute \( y = 30 \) back to find \( x \):
\[
x = 2 \times 30 = 60
\]

### Answer for Part 3b
The measure of \( \angle ADC \) is \( 60^\circ \), so the correct answer is:
- **C. \( 60^\circ \)**

Would you like more details or have any questions?

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#### Related Questions:
1. What would the measure of \( \angle CBD \) be if \( \angle ADC \) was three times \( \angle CBD \)?
2. How would you solve for the angles if \( \angle ADC \) and \( \angle CBD \) were supplementary instead of complementary?
3. If \( \angle ADC \) was half of \( \angle CBD \), what would their measures be?
4. Can you verify the complementary nature of two angles if only one angle measure is given?
5. How does knowing one angle in a complementary pair help find the other angle?

#### Tip:
Remember, complementary angles always add up to \( 90^\circ \), and supplementary angles add up to \( 180^\circ \).

Angles ADC and CBD are complementary, and ∠ADC is twice the size of ∠CBD. Which equation represents this relationship?

Learn how to solve for complementary angles where ∠ADC is twice the size of ∠CBD. This step-by-step guide uses algebraic equations to represent and solve the relationship between the two angles. Suitable for students in Grades 7-9.

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